Deck 3: Polynomial and Rational Functions

Question 1

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

- $$f ( x ) = - 15 x ^ { 4 } + \pi x ^ { 3 } + 1$$

A) Yes; degree 8
B) Yes; degree 7
C) No; $x ^ { 3 }$ has a non-integer coefficient
D) Yes; degree 4

Answer 1

Yes; degree 4

Question 2

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

- $7 ( x - 1 ) ^ { 11 } ( x + 1 ) ^ { 3 }$

A) Yes; degree 14
B) Yes; degree 11
C) Yes; degree 7
D) Yes; degree 77

Answer 2

Yes; degree 14

Question 3

Use transformations of the graph o $y = x ^ { 4 } \text { or } y = x ^ { 5 }$ to graph the function.

- $$f ( x ) = \frac { 1 } { 2 } ( x + 4 ) ^ { 4 } + 3$$

A)


B)


C)


D)

Answer 3

Question 4

Use transformations of the graph o $y = x ^ { 4 } \text { or } y = x ^ { 5 }$ to graph the function.

- $$f ( x ) = - 2 ( x - 2 ) ^ { 4 } + 4$$

A)


B)


C)


D)

Question 5

Use transformations of the graph o $y = x ^ { 4 } \text { or } y = x ^ { 5 }$ to graph the function.

- $$f ( x ) = ( x + 2 ) ^ { 4 } + 3$$

A)


B)


C)


D)

Question 6

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

- $f ( x ) = \frac { x ^ { 4 } - 7 } { x ^ { 3 } }$

A) Yes; degree -3
B) Yes; degree 3
C) No; it is a ratio of polynomials
D) Yes; degree 4

Question 7

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

- $f ( x ) = 5 - \frac { 3 } { x ^ { 6 } }$

A) No; x is raised to the negative 6 power
B) Yes; degree 6
C) Yes; degree $\frac { 1 } { 6 }$
D) Yes; degree -6

Question 8

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

- $f ( x ) = x ( x - 9 )$

A) Yes; degree 1
B) Yes; degree 2
C) Yes; degree 0
D) No; it is a product

Question 9

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

- $f ( x ) = - 14 x ^ { 3 } + 9 x ^ { 2 } - 7$

A) Yes; degree 6
B) Yes; degree 5
C) Yes; degree 3
D) No; the last term has no variable

Question 10

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.
f(x) = 5

A) No; it is a constant
B) Yes; degree 0
C) Yes; degree 1
D) No; it contains no variables

Question 11

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

- $f ( x ) = \frac { 6 } { 5 } - \frac { 1 } { 5 } x$

A) Yes; degree 0
B) Yes; degree 5
C) No; x has a fractional coefficient
D) Yes; degree 1

Question 12

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

- $f ( x ) = \sqrt { x } ( \sqrt { x } - 5 )$

A) Yes; degree 1
B) No; it is a product
C) No; x is raised to non-integer power
D) Yes; degree 2

Question 13

Use transformations of the graph o $y = x ^ { 4 } \text { or } y = x ^ { 5 }$ to graph the function.

- $f(x)=x^{4}-5$

A)


B)


C)


D)

Question 14

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

- $f ( x ) = 1 + \frac { 6 } { x }$

A) Yes; degree 0
B) Yes; degree 6
C) Yes; degree 1
D) No; x is raised to a negative power

Question 15

Use transformations of the graph o $y = x ^ { 4 } \text { or } y = x ^ { 5 }$ to graph the function.

- $f(x)=-2 x^{4}$

A)


B)


C)


D)

Question 16

Use transformations of the graph o $y = x ^ { 4 } \text { or } y = x ^ { 5 }$ to graph the function.

- $$f ( x ) = - \frac { 1 } { 3 } x ^ { 4 }$$

A)


B)


C)


D)

Question 17

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

- $f ( x ) = 5 x + 7 x ^ { 3 }$

A) Yes; degree 7
B) Yes; degree 1
C) Yes; degree 3
D) Yes; degree 5

Question 18

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

- $f ( x ) = \frac { 2 - x ^ { 4 } } { 9 }$

A) Yes; degree 1
B) No; x is a negative term
C) No; it is a ratio
D) Yes; degree 4

Question 19

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

- $$f ( x ) = x ^ { 3 / 2 } - x ^ { 6 } + 7$$

A) Yes; degree $3 / 2$
B) Yes; degree 3
C) Yes; degree 6
D) No; $\mathrm { x }$ is raised to non-integer $3 / 2$ power

Question 20

Use transformations of the graph o $y = x ^ { 4 } \text { or } y = x ^ { 5 }$ to graph the function.

- $f(x)=(x+3)^{4}$

A)

B)

C)

D)

Question 21

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1.

-Zeros: 3, multiplicity 2; -3, multiplicity 2; degree 4

A) $f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 18 x ^ { 2 } - 27 x + 81$
B) $f ( x ) = x ^ { 4 } + 6 x ^ { 3 } - 18 x ^ { 2 } + 27 x - 81$
C) $f ( x ) = x ^ { 4 } + 18 x ^ { 2 } + 81$
D) $f ( x ) = x ^ { 4 } - 18 x ^ { 2 } + 81$

Question 22

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1.

-Zeros: -5, -3, 3; degree 3

A) $f ( x ) = x ^ { 3 } - 9 x - 5 x ^ { 2 } + 45$
B) $f ( x ) = x ^ { 3 } + 9 x - 5 x ^ { 2 } - 45$
C) $f ( x ) = x ^ { 3 } + 9 x + 5 x ^ { 2 } + 45$
D) $f ( x ) = x ^ { 3 } - 9 x + 5 x ^ { 2 } - 45$

Question 23

Use transformations of the graph o $y = x ^ { 4 } \text { or } y = x ^ { 5 }$ to graph the function.

- $f(x)=x^{5}+4$

A)


B)


C)


D)

Question 24

Use transformations of the graph o $y = x ^ { 4 } \text { or } y = x ^ { 5 }$ to graph the function.

- $$f ( x ) = ( x - 3 ) ^ { 5 } + 2$$

A)


B)


C)


D)

Question 25

Use transformations of the graph o $y = x ^ { 4 } \text { or } y = x ^ { 5 }$ to graph the function.

- $f(x)=\frac{1}{2} x^{5}$

A)


B)


C)


D)

Question 26

Use transformations of the graph o $y = x ^ { 4 } \text { or } y = x ^ { 5 }$ to graph the function.

- $$f ( x ) = - 2 ( x + 3 ) ^ { 5 } + 2$$

A)


B)


C)


D)

Question 27

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at
each x -intercept.

- $$f ( x ) = 4 ( x - 3 ) ( x + 7 ) ^ { 4 }$$

A) 3, multiplicity 1, crosses x-axis; -7, multiplicity 4, touches x-axis
B) -3, multiplicity 1, touches x-axis; 7, multiplicity 4, crosses x-axis
C) -3, multiplicity 1, crosses x-axis; 7, multiplicity 4, touches x-axis
D) 3, multiplicity 1, touches x-axis; -7, multiplicity 4, crosses x-axis

Question 28

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1.

-Zeros: -5, multiplicity 2; -1, multiplicity 1; degree 3

A) $x ^ { 3 } + 11 x ^ { 2 } + 35 x + 25$
B) $x ^ { 3 } - 11 x ^ { 2 } + 10 x - 25$
C) $x ^ { 3 } + 10 x ^ { 2 } + 35 x + 25$
D) $x ^ { 3 } - 11 x ^ { 2 } + 35 x - 25$

Question 29

Use transformations of the graph o $y = x ^ { 4 } \text { or } y = x ^ { 5 }$ to graph the function.

- $$f ( x ) = \frac { 1 } { 2 } ( x - 3 ) ^ { 5 } + 4$$

A)


B)


C)


D)

Question 30

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at
each x -intercept.

- $$f ( x ) = \left( x + \frac { 1 } { 4 } \right) ^ { 4 } ( x + 1 ) ^ { 5 }$$

A) $\frac { 1 } { 4 }$ , multiplicity 4 , touches $x$ -axis; 1 , multiplicity 5 , crosses $x$ -axis
B) $\frac { 1 } { 4 }$ , multiplicity 4 , crosses $x$ -axis; 1 , multiplicity 5 , touches $x$ -axis
C) $- \frac { 1 } { 4 }$ , multiplicity 4 , touches $x$ -axis; $- 1$ , multiplicity 5 , crosses $x$ -axis
D) $- \frac { 1 } { 4 }$ , multiplicity 4 , crosses $x$ -axis; $- 1$ , multiplicity 5 , touches $x$ -axis

Question 31

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at
each x -intercept.

- $f ( x ) = 3 ( x - 6 ) ( x + 7 ) ^ { 3 }$

A) 6, multiplicity 1, crosses x-axis; -7, multiplicity 3, crosses x-axis
B) -6, multiplicity 1, touches x-axis; 7, multiplicity 3
C) -6, multiplicity 1, crosses x-axis; 7, multiplicity 3, crosses x-axis
D) 6, multiplicity 1, touches x-axis; -7, multiplicity 3

Question 32

Use transformations of the graph o $y = x ^ { 4 } \text { or } y = x ^ { 5 }$ to graph the function.

- $$f ( x ) = 4 - ( x - 2 ) ^ { 5 }$$

A)


B)


C)


D)

Question 33

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1.

-Zeros: -4, -3, -1, 5; degree 4

A) $x ^ { 4 } + 7 x ^ { 2 } - 60$
B) $x ^ { 4 } - 3 x ^ { 3 } - 21 x ^ { 2 } + 83 x - 60$
C) $x ^ { 4 } + 3 x ^ { 3 } - 21 x ^ { 2 } - 83 x - 60$
D) $x ^ { 4 } + 3 x ^ { 3 } - 21 x ^ { 2 } - 60 x - 60$

Question 34

Use transformations of the graph o $y = x ^ { 4 } \text { or } y = x ^ { 5 }$ to graph the function.

- $f(x)=-5 x^{5}$

A)


B)


C)


D)

Question 35

Use transformations of the graph o $y = x ^ { 4 } \text { or } y = x ^ { 5 }$ to graph the function.

- $$f ( x ) = ( x + 3 ) ^ { 5 }$$

A)


B)


C)


D)

Question 36

Use transformations of the graph o $y = x ^ { 4 } \text { or } y = x ^ { 5 }$ to graph the function.

- $$f ( x ) = 3 - ( x - 4 ) ^ { 4 }$$

A)


B)


C)


D)

Question 37

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1.

-Zeros: -1, 1, - 8; degree 3

A) $f ( x ) = x ^ { 3 } + 8 x ^ { 2 } + x + 8$
B) $f ( x ) = x ^ { 3 } - 8 x ^ { 2 } - x + 8$
C) $f ( x ) = x ^ { 3 } - 8 x ^ { 2 } + x - 8$
D) $f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - x - 8$

Question 38

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1.

-Zeros: 0, - 7, 6; degree 3

A) $f ( x ) = x ^ { 3 } + x ^ { 2 } + x - 42$
B) $f ( x ) = x ^ { 3 } + x ^ { 2 } + x + 42$
C) $f ( x ) = x ^ { 3 } + x ^ { 2 } - 42 x$
D) $f ( x ) = x ^ { 3 } + x ^ { 2 } + 42 x$

Question 39

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at
each x -intercept.

- $f ( x ) = 3 \left( x ^ { 2 } + 5 \right) ( x + 6 ) ^ { 2 }$

A) -6, multiplicity 2, touches x-axis
B) -5, multiplicity 1, touches x-axis; -6, multiplicity 2, crosses x-axis
C) -6, multiplicity 2, crosses x-axis
D) -5, multiplicity 1, crosses x-axis; -6, multiplicity 2, touches x-axis

Question 40

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1.

-Zeros: -3, -2, 3; degree 3

A) $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } + 9 x + 18$
B) $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 9 x - 18$
C) $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } + 9 x - 18$
D) $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 9 x + 18$

Question 41

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at
each x -intercept.

- $$f ( x ) = \left( x + \frac { 1 } { 4 } \right) ^ { 2 } \left( x ^ { 2 } + 7 \right) ^ { 3 }$$

A) $- \frac { 1 } { 4 }$ , multiplicity 2 , touches $x$ -axis
B) $- \frac { 1 } { 4 }$ , multiplicity 2 , touches $x$ -axis; $- 7$ , multiplicity 3 , crosses $x$ -axis
C) $- \frac { 1 } { 4 }$ , multiplicity 2 , crosses $x$ -axis
D) $\frac { 1 } { 4 }$ , multiplicity 2 , touches $x$ -axis; 7 , multiplicity 3 , crosses $x$ -axis

Question 42

Find the x- and y-intercepts of f.

- $$f ( x ) = x ^ { 2 } ( x - 4 ) ( x - 1 )$$

A) $x$ -intercepts: $0 , - 4 , - 1 ; y$ -intercept: 0
B) $x$ -intercepts: $0,4,1$ ; y-intercept: 4
C) $x$ -intercepts: $0,4,1$ ; y-intercept: 0
D) $x$ -intercepts: $0 , - 4 , - 1 ; y$ -intercept: 4

Question 43

Find the x- and y-intercepts of f.

- $$f ( x ) = ( x + 5 ) ( x - 4 ) ( x + 4 )$$

A) $x$ -intercepts: $- 5 , - 4,4 ; y$ -intercept: 80
B) x-intercepts: $- 5 , - 4,4$ ; y-intercept: $- 80$
C) $x$ -intercepts: $- 4,4,5 ; y$ -intercept: 80
D) $x$ -intercepts: $- 4,4,5 ; y$ -intercept: $- 80$

Question 44

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at
each x -intercept.

- $$f ( x ) = \frac { 1 } { 5 } x ^ { 4 } \left( x ^ { 2 } - 3 \right)$$

A) 0 , multiplicity 4 , touches $x$ -axis

B) 0 , multiplicity 4 , touches $x$ -axis;
$\sqrt { 3 }$ , multiplicity 1 , crosses $x$ -axis;
$- \sqrt { 3 }$ , multiplicity 1 , crosses $x$ -axis

C) 0 , multiplicity 4 , crosses $x$ -axis;
$\sqrt { 3 }$ , multiplicity 1 , touches $x$ -axis;
$- \sqrt { 3 }$ , multiplicity 1 , touches $x$ -axis

D) 0, multiplicity 4 , crosses $x$ -axis

Question 45

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at
each x -intercept.

- $$f ( x ) = 2 \left( x ^ { 2 } + 1 \right) \left( x ^ { 2 } + 6 \right) ^ { 2 }$$

A) No real zeros
B) $- 1$ , multiplicity 1 , touches $x$ -axis; $- 6$ , multiplicity 2 , crosses $x$ -axis
C) 1 , multiplicity 1 , crosses $x$ -axis; $- 1$ , multiplicity 1 , crosses $x$ -axis; $\sqrt { 6 }$ , multiplicity 2 , touches $x$ -axis; $- \sqrt { 6 }$ , multiplicity 2 , touches $x$ -axis
D) $- 1$ , multiplicity 1 , crosses $x$ -axis; $- 6$ , multiplicity 2 , touches $x$ -axis

Question 46

Find the power function that the graph of f resembles for large values of $| \mathbf { x } |$

- $$f ( x ) = ( x + 8 ) ^ { 2 }$$

A) $y = x ^ { 16 }$
B) $y = x ^ { 2 }$
C) $y = x ^ { 8 }$
D) $y = x ^ { 64 }$

Question 47

Find the x- and y-intercepts of f.

- $$f ( x ) = ( x + 1 ) ( x - 5 ) ( x - 1 ) ^ { 2 }$$

A) $x$ -intercepts: $- 1,1,5 ; y$ -intercept: 5
B) $x$ -intercepts: $- 1,1,5 ; y$ -intercept: $- 5$
C) $x$ -intercepts: $- 1,1 , - 5 ; y$ -intercept: $- 5$
D) $x$ -intercepts: $- 1,1 , - 5 ; y$ -intercept: 5

Question 48

Find the x- and y-intercepts of f.

- $$f ( x ) = - x ^ { 2 } ( x + 4 ) \left( x ^ { 2 } + 1 \right)$$

A) $x$ -intercepts: $- 4 , - 1,0,1$ ; y-intercept: 0
B) $x$ -intercepts: $- 4,0 ; y$ -intercept: 0
C) $x$ -intercepts: $- 4 , - 1,0$ ; y-intercept: 4
D) $x$ -intercepts: $- 4 , - 1,0$ ; y-intercept: $- 4$

Question 49

Find the x- and y-intercepts of f.

- $$f ( x ) = ( x - 2 ) ^ { 2 } \left( x ^ { 2 } - 25 \right)$$

A) $x$ -intercepts: $- 5,2,5$ ; y-intercept: 100
B) x-intercepts: 2, 25; y-intercept: 50
C) x-intercepts: $- 2 , - 25$ ; y-intercept: 50
D) $x$ -intercepts: $- 5,2,5 ; y$ -intercept: $- 100$

Question 50

Find the x- and y-intercepts of f.

- $$f ( x ) = ( x + 13 ) ^ { 2 }$$

A) $x$ -intercept: $- 13$ ; $y$ -intercept: 169
B) $x$ -intercept: $- 13 ; y$ -intercept: 0
C) $x$ -intercept: 13; $y$ -intercept: 169
D) $x$ -intercept: $13 ; y$ -intercept: 0

Question 51

Find the x- and y-intercepts of f.

- $$f ( x ) = ( x - 4 ) ( x - 1 )$$

A) $x$ -intercepts: 4,1 ; y-intercept: $- 5$
B) $x$ -intercepts: 4,1 ; y-intercept: 4
C) $x$ -intercepts: $- 4 , - 1 ; y$ -intercept: $- 5$
D) x-intercepts: $- 4 , - 1 ; \mathrm { y }$ -intercept: 4

Question 52

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at
each x -intercept.

- $$f ( x ) = \frac { 1 } { 5 } x \left( x ^ { 2 } - 5 \right)$$

A) 0 , multiplicity 1

B) $\sqrt { 5 }$ , multiplicity 1 , touches $x$ -axis;
$- \sqrt { 5 }$ , multiplicity 1 , touches $x$ -axis

C) 0 , multiplicity 1 , crosses x-axis;
$\sqrt { 5 }$ , multiplicity 1 , touches $x$ -axis;
$- \sqrt { 5 }$ , multiplicity 1 , crosses $x$ -axis

D) 0 , multiplicity 1 , touches $x$ -axis;
$\sqrt { 5 }$ , multiplicity 1 , crosses $x$ -axis;
$- \sqrt { 5 }$ , multiplicity 1 , touches $x$ -axis

Question 53

Find the x- and y-intercepts of f.

- $$f ( x ) = - x ^ { 2 } ( x + 6 ) \left( x ^ { 2 } - 1 \right)$$

A) $x$ -intercepts: $- 6 , - 1,0,1 ; y$ -intercept: $- 6$
B) $x$ -intercepts: $- 6,0,1 ; y$ -intercept: $- 6$
C) x-intercepts: $- 6 , - 1,0,1$ ; y-intercept: 0
D) x-intercepts: $- 1,0,1,6$ ; y-intercept: 0

Question 54

Find the power function that the graph of f resembles for large values of $| \mathbf { x } |$

- $$f ( x ) = ( x - 3 ) ^ { 3 }$$

A) $y = x ^ { - 3 }$
B) $y = x ^ { 3 }$
C) $y = x ^ { 9 }$
D) $y = x ^ { - 27 }$

Question 55

Find the x- and y-intercepts of f.

- $$f ( x ) = 4 x ^ { 2 } ( x + 3 ) ^ { 3 }$$

A) $x$ -intercepts: $0 , - 3$ ; y-intercept: 4
B) x-intercepts: $0 , - 3 ; y$ -intercept: 0
C) $x$ -intercepts: 0, $3 ; y$ -intercept: 4
D) x-intercepts: 0,3 ; y-intercept: 0

Question 56

Find the power function that the graph of f resembles for large values of $| \mathbf { x } |$

- $$f ( x ) = 3 x - x ^ { 3 }$$

A) $y = x ^ { 2 }$
B) $y = x ^ { 4 }$
C) $y = x ^ { 3 }$
D) $y = - x ^ { 3 }$

Question 57

Find the power function that the graph of f resembles for large values of $| \mathbf { x } |$

- $$f ( x ) = ( x + 12 ) ^ { 6 } ( x - 3 ) ^ { 3 }$$

A) $y = x ^ { 6 }$
B) $y = x ^ { 3 }$
C) $y = x ^ { 18 }$
D) $y = x ^ { 9 }$

Question 58

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at
each x -intercept.

- $$f ( x ) = \frac { 1 } { 5 } x ^ { 4 } \left( x ^ { 2 } - 3 \right) ( x - 3 )$$

A) 0 , multiplicity 4 , touches $x$ -axis;
3 , multiplicity 1 , touches $x$ -axis
$\sqrt { 3 }$ , multiplicity 1 , crosses $x$ -axis;
$- \sqrt { 3 }$ , multiplicity 1 , crosses $x$ -axis

B) 0, multiplicity 4 , crosses $x$ -axis;
3 , multiplicity 1 , crosses $x$ -axis;

C) 0 , multiplicity 4 , crosses $x$ -axis;
3 , multiplicity 1 , touches $x$ -axis;
$\sqrt { 3 }$ , multiplicity 1 , touches $x$ -axis;
$- \sqrt { 3 }$ , multiplicity 1 , touches $x$ -axis

D) 0 , multiplicity 4 , touches $x$ -axis;
3 , multiplicity 1 , crosses $x$ -axis

Question 59

Find the power function that the graph of f resembles for large values of $| \mathbf { x } |$

- $$f ( x ) = - x ^ { 2 } ( x + 4 ) ^ { 3 } \left( x ^ { 2 } - 1 \right)$$

A) $y = x ^ { 3 }$
B) $y = x ^ { 2 }$
C) $y = - x ^ { 7 }$
D) $y = x ^ { 7 }$

Question 60

Find the x- and y-intercepts of f.

- $f ( x ) = 5 x - x ^ { 3 }$

A) x-intercepts: $0 , \sqrt { 5 } , - \sqrt { 5 } ; y$ -intercept: 0
B) x-intercepts: $0 , \sqrt { 5 } , - \sqrt { 5 } ; y$ -intercept: 5
C) $x$ -intercepts: $0 , - 5 ; y$ -intercept: 5
D) $x$ -intercepts: $0 , - 5 ; y$ -intercept: 0

Question 61

Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis.

- $$f ( x ) = ( x - 2 ) ^ { 2 } ( x + 4 ) ^ { 2 }$$

A) above the $x$ -axis: $( - 4,2 )$
below the x-axis: $( - \infty , - 4 ) , ( 2 , \infty )$

B) above the $x$ -axis: no intervals
below the x-axis: $( - \infty , - 4 ) , ( - 4,2 ) , ( 2 , \infty )$

C) above the $x$ -axis: $( - \infty , - 4 ) , ( - 4,2 ) , ( 2 , \infty )$
below the $x$ -axis: no intervals

D) above the $x$ -axis: $( - \infty , - 4 ) , ( 2 , \infty )$
below the x-axis: $( - 4,2 )$

Question 62

Analyze the graph of the given function f as follows:
(a) Determine the end behavior: find the power function that the graph of f resembles for large values of | (b) Find the x- and y-intercepts of the graph.
(c) Determine whether the graph crosses or touches the x-axis at each x-intercept.
(d) Graph f using a graphing utility.
(e) Use the graph to determine the local maxima and local minima, if any exist. Round turning points to two decimal places.
(f) Use the information obtained in (a) - (e) to draw a complete graph of f by hand. Label all intercepts and turning points.
(g) Find the domain of f. Use the graph to find the range of f.
(h) Use the graph to determine where f is increasing and where f is decreasing.

Question 63

Determine the maximum number of turning points of f.

- $f ( x ) = ( x - 2 ) ^ { 2 } ( x + 4 ) ^ { 2 }$

A) 3
B) 2
C) 4
D) 1

Question 64

Analyze the graph of the given function f as follows:
(a) Determine the end behavior: find the power function that the graph of f resembles for large values of | (b) Find the x- and y-intercepts of the graph.
(c) Determine whether the graph crosses or touches the x-axis at each x-intercept.
(d) Graph f using a graphing utility.
(e) Use the graph to determine the local maxima and local minima, if any exist. Round turning points to two decimal places.
(f) Use the information obtained in (a) - (e) to draw a complete graph of f by hand. Label all intercepts and turning points.
(g) Find the domain of f. Use the graph to find the range of f.
(h) Use the graph to determine where f is increasing and where f is decreasing.

Question 65

Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis.

- $$f ( x ) = ( x + 15 ) ^ { 2 }$$

A) above the $x$ -axis: $( - \infty , - 15 )$
below the $x$ -axis: $( - 15 , \infty )$

B) above the $x$ -axis: $( - \infty , - 15 ) , ( - 15 , \infty )$
below the $x$ -axis: no intervals

C) above the $x$ -axis: $( - 15 , \infty )$
below the $x$ -axis: $( - \infty , - 15 )$

D) above the $x$ -axis: no intervals
below the $x$ -axis: $( - \infty , - 15 ) , ( - 15 , \infty )$

Question 66

Determine the maximum number of turning points of f.

- $f ( x ) = 9 x - x ^ { 3 }$

A) 2
B) 3
C) 4
D) 1

Question 67

Analyze the graph of the given function f as follows:
(a) Determine the end behavior: find the power function that the graph of f resembles for large values of | (b) Find the x- and y-intercepts of the graph.
(c) Determine whether the graph crosses or touches the x-axis at each x-intercept.
(d) Graph f using a graphing utility.
(e) Use the graph to determine the local maxima and local minima, if any exist. Round turning points to two decimal places.
(f) Use the information obtained in (a) - (e) to draw a complete graph of f by hand. Label all intercepts and turning points.
(g) Find the domain of f. Use the graph to find the range of f.
(h) Use the graph to determine where f is increasing and where f is decreasing.

Question 68

Analyze the graph of the given function f as follows:
(a) Determine the end behavior: find the power function that the graph of f resembles for large values of | (b) Find the x- and y-intercepts of the graph.
(c) Determine whether the graph crosses or touches the x-axis at each x-intercept.
(d) Graph f using a graphing utility.
(e) Use the graph to determine the local maxima and local minima, if any exist. Round turning points to two decimal places.
(f) Use the information obtained in (a) - (e) to draw a complete graph of f by hand. Label all intercepts and turning points.
(g) Find the domain of f. Use the graph to find the range of f.
(h) Use the graph to determine where f is increasing and where f is decreasing.

Question 69

Solve the problem.

-Which of the following polynomial functions might have the graph shown in the illustration below?

A) $f ( x ) = x ( x - 2 ) ( x - 1 ) ^ { 2 }$
B) $f ( x ) = x ( x - 2 ) ^ { 2 } ( x - 1 )$
C) $f ( x ) = x ^ { 2 } ( x - 2 ) ( x - 1 )$
D) $f ( x ) = x ^ { 2 } ( x - 2 ) ^ { 2 } ( x - 1 ) ^ { 2 }$

Question 70

Determine the maximum number of turning points of f.

- $f ( x ) = - x ^ { 2 } ( x + 6 ) ^ { 3 } \left( x ^ { 2 } - 1 \right)$

A) 7
B) 2
C) 5
D) 6

Question 71

Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis.

- $$f ( x ) = \left( x + \frac { 1 } { 8 } \right) ^ { 2 } ( x - 2 ) ^ { 5 }$$

A) above the $x$ -axis: $\left( - \frac { 1 } { 8 } , 2 \right)$
below the x-axis: $\left( - \infty , - \frac { 1 } { 8 } \right) , ( 2 , \infty )$

B) above the x-axis: $\left( - \infty , - \frac { 1 } { 8 } \right)$ ,
below the $x$ -axis: $\left( - \frac { 1 } { 8 } , 2 \right)$

C) above the $x$ -axis: $\left( - \infty , - \frac { 1 } { 8 } \right) , \left( - \frac { 1 } { 8 } , 2 \right)$
below the $x$ -axis: $( 2 , \infty )$

D) above the $x$ -axis: $( 2 , \infty )$
below the $x$ -axis: $\left( - \infty , - \frac { 1 } { 8 } \right) , \left( - \frac { 1 } { 8 } , 2 \right)$

Question 72

Solve the problem.
The profits (in millions) for a company for 8 years was as follows: Find the cubic function of best fit to the data.

Question 73

Find the indicated intercept(s) of the graph of the function.2133:2139

- $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 6 x + 8 ; x - 4$

A) Yes
B) No

Question 74

Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis.

- $$f ( x ) = ( x - 3 ) ^ { 3 }$$

A) above the $x$ -axis: $( 3 , \infty )$
below the x-axis: $( - \infty , 3 )$

B) above the $x$ -axis: $( - \infty , 3 )$
below the $x$ -axis: $( 3 , \infty )$

C) above the $x$ -axis: no intervals
below the $x$ -axis: $( - \infty , 3 ) , ( 3 , \infty )$

D) above the $x$ -axis: $( - \infty , 3 ) , ( 3 , \infty )$
below the x-axis: no intervals

Question 75

Solve the problem.
For the polynomial function f(x) a) Find the x- and y-intercepts of the graph of f. Round to two decimal places, if necessary.
b) Determine whether the graph crosses or touches the x-axis at each x-intercept.
c) End behavior: find the power function that the graph of f resembles for large values of |x d) Use a graphing utility to graph the function.Approximate the local maxima rounded to two decimal places, if
necessary. Approximate the local minima rounded to two decimal places, if necessary.
e) Determine the number of turning points on the graph.
f) Put all the information together, and connect the points with a smooth, continuous curve to obtain the graph of f.

Question 76

Analyze the graph of the given function f as follows:
(a) Determine the end behavior: find the power function that the graph of f resembles for large values of | (b) Find the x- and y-intercepts of the graph.
(c) Determine whether the graph crosses or touches the x-axis at each x-intercept.
(d) Graph f using a graphing utility.
(e) Use the graph to determine the local maxima and local minima, if any exist. Round turning points to two decimal places.
(f) Use the information obtained in (a) - (e) to draw a complete graph of f by hand. Label all intercepts and turning points.
(g) Find the domain of f. Use the graph to find the range of f.
(h) Use the graph to determine where f is increasing and where f is decreasing.

Question 77

Solve the problem.

-The amount of water (in gallons) in a leaky bathtub is given in the table below. Using a graphing utility, fit the data to a third degree polynomial (or a cubic). Then approximate the time at which there is maximum amount
Of water in the tub, and estimate the time when the water runs out of the tub. Express all your answers rounded
To two decimal places. $$\begin{array} { c | c c c c c c c c } \mathrm { t } \text { (in minutes) } & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\\hline \mathrm { V } \text { ( in gallons) } & 20 & 26 & 45 & 63 & 86 & 94 & 90 & 67\end{array}$$

A) maximum amount of water after 5.37 minutes; water runs out after 11.06 minutes
B) maximum amount of water after 8.23 minutes; water runs out after 19.73 minutes
C) maximum amount of water after 5.31 minutes; water runs out after 8.23 minutes
D) maximum amount of water after 5.31 minutes; water never runs out

Question 78

Analyze the graph of the given function f as follows:
(a) Determine the end behavior: find the power function that the graph of f resembles for large values of | (b) Find the x- and y-intercepts of the graph.
(c) Determine whether the graph crosses or touches the x-axis at each x-intercept.
(d) Graph f using a graphing utility.
(e) Use the graph to determine the local maxima and local minima, if any exist. Round turning points to two decimal places.
(f) Use the information obtained in (a) - (e) to draw a complete graph of f by hand. Label all intercepts and turning points.
(g) Find the domain of f. Use the graph to find the range of f.
(h) Use the graph to determine where f is increasing and where f is decreasing.

Question 79

Use the Factor Theorem to determine whether x - c is a factor of f(x).

- $f ( x ) = x ^ { 3 } + 7 x ^ { 2 } - 16 x + 18 ; x + 9$

A) Yes
B) No

Question 80

Analyze the graph of the given function f as follows:
(a) Determine the end behavior: find the power function that the graph of f resembles for large values of | (b) Find the x- and y-intercepts of the graph.
(c) Determine whether the graph crosses or touches the x-axis at each x-intercept.
(d) Graph f using a graphing utility.
(e) Use the graph to determine the local maxima and local minima, if any exist. Round turning points to two decimal places.
(f) Use the information obtained in (a) - (e) to draw a complete graph of f by hand. Label all intercepts and turning points.
(g) Find the domain of f. Use the graph to find the range of f.
(h) Use the graph to determine where f is increasing and where f is decreasing.