Deck 4: Functions

Question 1

Evaluate g(t)- g(9)if g(t)= 12t² - 6t + 3.

A)g(t)- g(9)= 12t² - 918 + 6t
B)g(t)- g(9)= 6t² - 918t + 12
C)g(t)- g(9)= 12t² - 918t - 6
D)g(t)- g(9)= 6t² + 12t - 918
E)g(t)- g(9)= 12t² - 6t - 918

Answer 1

g(t)- g(9)= 12t² - 6t - 918

Question 2

Evaluate the function $$f ( x ) = \left\{ \begin{array} { c } 9 - 2 x , x < - 2 \\0 , \quad - 2 \leq x \leq 2 \\x ^ { 2 } + 8 , x > 2\end{array} \right.$$ at f(7).

A)f(7)= 61
B)f(7)= 58
C)f(7)= 57
D)f(7)= 59
E)f(7)= 60

Answer 2

f(7)= 57

Question 3

Complete the table. $$f ( x ) = \left\{ \begin{array} { l } - \frac { 1 } { 2 } x + 4 , x \leq 0 \\( x - 2 ) ^ { 2 } , x > 0\end{array} \right.$$
$$\begin{array} { | l | l | l | l | l | l | } \hline x & - 6 & - 4 & 0 & 1 & 4 \\\hline f ( x ) & & & & & \\\hline\end{array}$$

A) $$\begin{array} { | l | l | l | l | l | l | } \hline x & - 6 & - 4 & 0 & 1 & 4 \\\hline f ( x ) & 9 & 7 & - 3 & 1 & 4 \\\hline\end{array}$$
B) $$\begin{array} { | l | l | l | l | l | l | } \hline x & - 6 & - 4 & 0 & 1 & 4 \\\hline f ( x ) & 7 & 6 & 4 & 3 & 6 \\\hline\end{array}$$
C) $$\begin{array} { | l | l | l | l | l | l | } \hline x & - 6 & - 4 & 0 & 1 & 4 \\\hline f ( x ) & 7 & 6 & 4 & 1 & 4 \\\hline\end{array}$$
D) $$\begin{array} { | l | l | l | l | l | l | } \hline x & - 6 & - 4 & 0 & 1 & 4 \\\hline f ( x ) & 7 & 6 & 0 & 1 & 4 \\\hline\end{array}$$
E) $$\begin{array} { | l | l | l | l | l | l | } \hline x & - 6 & - 4 & 0 & 1 & 4 \\\hline f ( x ) & 7 & 8 & 4 & 4 & 1 \\\hline\end{array}$$

Answer 3

$$\begin{array} { | l | l | l | l | l | l | } \hline x & - 6 & - 4 & 0 & 1 & 4 \\\hline f ( x ) & 7 & 6 & 4 & 1 & 4 \\\hline\end{array}$$

Question 4

Which set of ordered pairs represents a function from A to B
A = {3,2,4,1} and B = {-4,-5,3,2,4}

A){(3,-4), (2,-5), (4,-4), (3,-5)}
B){(3,-4), (4,4), (2,-5), (1,3), (2,2)}
C){(3,4), (1,3), (2,2)}
D){(3,2), (2,-4), (4,3), (1,4)}
E){(3,-4), (2,2), (1,3)}

Question 5

Which of the following equation does not represent y as a function of x

A)y² = 1 - x
B)y = x² + 1
C)x² + y = 1
D)y = x² + x - 1
E)y = x² - 1

Question 6

Evaluate ?f(16)if $$f ( x ) = \sqrt { x + 9 } + 1$$ .

A)f(16)= 5
B)f(16)= 7
C)f(16)= 4
D)f(16)= 8
E)f(16)= 6

Question 7

Complete the table. $$h ( t ) = \frac { 1 } { 2 } | t + 3 |$$
$$\begin{array} { | l | l | l | l | l | l | } \hline t & - 11 & - 9 & 0 & - 5 & - 1 \\\hline h ( t ) & & & & & \\\hline\end{array}$$

A)
$$\begin{array} { | l | l | l | l | l | l | } \hline t & - 11 & - 9 & 0 & - 5 & - 1 \\\hline h ( t ) & 3 & 4 & - 3 & 1 & 1 \\\hline\end{array}$$
B) $$\begin{array} { | l | l | l | l | l | l | } \hline t & - 11 & - 9 & 0 & - 5 & - 1 \\\hline \\ h ( t ) & 4 & 3 & \frac{3}{2}& 1 & 1 \\\\\hline\end{array}$$ .
C) $$\begin{array} { | l | l | l | l | l | l | } \hline t & - 11 & - 9 & 0 & - 5 & - 1 \\\hline \\ h ( t ) & 4 & 3 & 1 & \frac{3}{2}& 1 \\\\\hline\end{array}$$
D) $$\begin{array} { | l | l | l | l | l | l | } \hline t & - 11 & - 9 & 0 & - 5 & - 1 \\\hline \\ h ( t ) & 4 & 3 & \frac{3}{2}& 1 & 1 \\\\\hline\end{array}$$
E) $$\begin{array} { | l | l | l | l | l | l | } \hline t & - 11 & - 9 & 0 & - 5 & - 1 \\\hline h ( t ) & 4 & 3 & 0 & 1 & 1 \\\hline\end{array}$$

Question 8

Evaluate the function $$f ( x ) = \left\{ \begin{array} { c } 4 x - 2 , x < - 1 \\7 , \quad - 1 \leq x \leq 1 \\x ^ { 2 } , x > 1\end{array} \right.$$ at $f \left( - \frac { 1 } { 2 } \right)$ . ?

A) $$f \left( - \frac { 1 } { 2 } \right) = - 10$$
B) $f \left( - \frac { 1 } { 2 } \right) = 10$
C) $f \left( - \frac { 1 } { 2 } \right) = - 7$
D) $$f \left( - \frac { 1 } { 2 } \right) = - 4$$
E) $f \left( - \frac { 1 } { 2 } \right) = 7$

Question 9

Evaluate f(11)if $$f ( x ) = \frac { | x | } { x }$$ .

A)f(11)= -1
B)f(11)= 2
C)f(11)= 0
D)f(11)= 1
E)f(11)= 3

Question 10

Evaluate f(0)if $$f ( x ) = \left\{ \begin{array} { l l } 9 x + 6 , & x < 0 \\9 x + 9 , & x \geq 0\end{array} \right.$$ .

A)f(0)= -9
B)f(0)= 6
C)f(0)= 9
D)f(0)= -6
E)f(0)= 0

Question 11

Evaluate q(4)if $$q ( x ) = \frac { 1 } { \left( x ^ { 2 } - 7 \right) }$$ .

A)q(4)= $\frac { 1 } { 13 }$
B)q(4)= $\frac { 1 } { 11 }$
C)q(4)= $\frac{1}{9}$
D)q(4)= $\frac { 1 } { 12 }$
E)q(4)= $\frac { 1 } { 10 }$

Question 12

Evaluate S(3)if S(r)= 4πr².

A)S(3)= 40
B)S(3)= 9
C)S(3)= 38
D)S(3)= 36
E)S(3)= 37

Question 13

Evaluate f(-4)if $$f ( x ) = \left\{ \begin{array} { l } x ^ { 2 } + 5 , \quad x < 1 \\5 x ^ { 2 } + 5 , \quad x \geq 1\end{array} \right.$$ .

A)f(-4)= 19
B)f(-4)= 11
C)f(-4)= 16
D)f(-4)= 23
E)f(-4)= 21

Question 14

Which set of ordered pairs represents a function from A to B
A = {a,b,c} and B = {4,3,1,2}

A){(a,4), (b,3)}
B){(a,2), (c,3), (b,4 )}
C){(a,4), (c,1)}
D){(a,1), (c,3), (c,1), (b,4)}
E){(a,4), (c,3), (c,1), (b,1)}

Question 15

Complete the table. $$f ( s ) = \frac { | s - 2 | } { s - 2 }$$
$$\begin{array} { | l | l | l | l | l | l | } \hline \\ s & 0 & 4 & \frac { 9 } { 2 } & \frac { 13 } { 2 } & 7 \\\\\hline f ( s ) & & & & & \\\hline\end{array}$$

A) $$\begin{array} { | l | l | l | l | l | l | } \hline \\ s & 0 & 4 & \frac { 9 } { 2 } & \frac { 13 } { 2 } & 7 \\\\\hline f ( s ) & - 1 & 1 & 1 & 1 & 1\\\hline\end{array}$$
B) $$\begin{array} { | l | l | l | l | l | l | } \hline \\s & 0 & 4 & \frac { 9 } { 2 } & \frac { 13 } { 2 } & 7 \\\\\hline f ( s ) & - 1 & 1 & 1 & 3&1 \\\hline\end{array}$$
C) $$\begin{array} { | l | l | l | l | l | l | } \hline \\s & 0 & 4 & \frac { 9 } { 2 } & \frac { 13 } { 2 } & 7 \\\\\hline f ( s ) & - 1 & 1 & 3 & 1&1 \\\hline\end{array}$$
D) $$\begin{array} { | l | l | l | l | l | l | } \hline \\s & 0 & 4 & \frac { 9 } { 2 } & \frac { 13 } { 2 } & 7 \\\\\hline f ( s ) & 1 & 1 & 3 & 1&1 \\\hline\end{array}$$
E) $$\begin{array} { | l | l | l | l | l | l | } \hline \\s & 0 & 4 & \frac { 9 } { 2 } & \frac { 13 } { 2 } & 7 \\\\\hline f ( s ) & - 1 & 3 & 1 & 1&1 \\\hline\end{array}$$

Question 16

Evaluate f(-7)if f(x)= 12x - 8.

A)f(-7)= -89
B)f(-7)= -91
C)f(-7)= -88
D)f(-7)= -92
E)f(-7)= -90

Question 17

Evaluate f(7)if f(x)= 4x - 1.

A)f(7)= 27
B)f(7)= 26
C)f(7)= 29
D)f(7)= 25
E)f(7)= 28

Question 18

Complete the table. f(x)= x² - 3
$$\begin{array} { | l | l | l | l | l | l | } \hline x & - 3 & - 1 & 0 & 4 & 5 \\\hline f ( x ) & & & & & \\\hline\end{array}$$

A) $$\begin{array} { | l | l | l | l | l | l | } \hline x & - 3 & - 1 & 0 & 4 & 5 \\\hline f ( x ) & 6 & - 2 & 13 & - 3 & 22 \\\hline\end{array}$$
B) $$\begin{array} { | l | l | l | l | l | l | } \hline x & - 3 & - 1 & 0 & 4 & 5 \\\hline f ( x ) & 6 & - 2 & - 3 & 22 & 13 \\\hline\end{array}$$
C) $$\begin{array} { | l | l | l | l | l | l | } \hline x & - 3 & - 1 & 0 & 4 & 5 \\\hline f ( x ) & - 2 & 6 & - 3 & 13 & 22 \\\hline\end{array}$$
D) $$\begin{array} { | l | l | l | l | l | l | } \hline x & - 3 & - 1 & 0 & 4 & 5 \\\hline f ( x ) & 6 & - 2 & 0 & 13 & 22 \\\hline\end{array}$$
E) $$\begin{array} { | l | l | l | l | l | l | } \hline x & - 3 & - 1 & 0 & 4 & 5 \\\hline f ( x ) & 6 & - 2 & - 3 & 13 & 22 \\\hline\end{array}$$

Question 19

Evaluate g(s + 2)if g(y)= 12 - 5y.

A)g(s + 2)= -2 + 5s
B)g(s + 2)= -2 - 5s
C)g(s + 2)= 2 + 5s
D)g(s + 2)= 2 - 5s
E)g(s + 2)= 12 - 5s

Question 20

Which of the following equation represents y as a function of x

A)y² = 9 - x
B)y³ = x + 9
C)y² = x + 9
D)x² + y = 9
E)x2 + y² = 9

Question 21

Find the domain of the function.
F(x)= 2x² + 4x - 5

A)All real numbers x such that x > 0
B)All real numbers x
C)All real numbers x such that x < 0
D)Non-negative real numbers x
E)Non-negative real numbers x except x = 0

Question 22

Find the difference quotient and simplify your answer.
F(x)= 5x - x², $\frac { f ( 6 + h ) - f ( 6 ) } { h }$ ,h ? 0

A) $\frac { f ( 6 + h ) - f ( 6 ) } { h } = - h - 6$ ,h ? 0
B) $\frac { f ( 6 + h ) - f ( 6 ) } { h } = - h - 4$ ,h ? 0
C) $\frac { f ( 6 + h ) - f ( 6 ) } { h } = - h - 3$ ,h? 0
D) $\frac { f ( 6 + h ) - f ( 6 ) } { h } = - h - 7$ ,h ? 0
E) $\frac { f ( 6 + h ) - f ( 6 ) } { h } = - h - 5$ ,h ? 0

Question 23

Find the domain of the function. $$h ( t ) = \frac { 5 } { t }$$

A)All real numbers t except t = 0
B)Negative real numbers t
C)All real numbers t such that t > 0
D)Non-negative real numbers t
E)All real numbers t such that t = 0

Question 24

Does the table describe a function? Input value
$$\begin{array} { | l | l | l | l | l | l | } \hline \text { Input value } & - 5 & - 3 & 0 & 3 & 5 \\\hline \text { Output value } & - 3 & - 3 & - 3 & - 3 & - 3 \\\hline\end{array}$$

A)No
B)Yes

Question 25

Find all real values of x such that f(x)= 0.
F(x)= 12 - 2x

A)x = 6
B)x = 5
C)x = 7
D)x = 4
E)x = 8

Question 26

A rectangle is bounded by the x-axis and the semicircle $y = \sqrt { 49 - x ^ { 2 } }$ (see figure).Select the area A of the rectangle as a function of x,and determine the domain of the function.?

A) $A ( x ) = 2 | x | \sqrt { 49 - x ^ { 2 } }$ ,-7 ? x ? 7
B) $A ( x ) = - 2 x \sqrt { 49 - x ^ { 2 } }$ ,-7 ? x? 7
C) $A ( x ) = x \sqrt { 49 - x ^ { 2 } }$ ,x ? 0
D) $A ( x ) = 2 x \sqrt { 49 - x ^ { 2 } }$ ,x ? 0
E) $A ( x ) = | x | \sqrt { 49 - x ^ { 2 } }$ ,all real numbers

Question 27

Evaluate the function at the specified value of the independent variable and simplify. g(s)= 3s + 1G(-18)

A)g(-18)= -55
B)g(-18)= -54s + 3
C)g(-18)= -18s - 1
D)g(-18)= -18s + 1
E)g(-18)= -53

Question 28

Find all real value of x such that f (x)= 0. $$f ( x ) = \frac { - 9 x + 8 } { 5 }$$

A)x = $\frac { 8 } { 9 }$
B)x = $\frac { 8 } { 45 }$
C)x = ± $\frac { 8 } { 9 }$
D)x = $- \frac { 8 } { 9 }$
E)x = ± $\frac { 8 } { 45 }$

Question 29

Find all real values of x such that f(x)= 0.
F(x)= x² - 8x - 20

A)x = -10,2
B)x = -10,-2
C)x = 2,10
D)x = -2,10
E)x = -8,8

Question 30

Find all real values of x such that f(x)= 0
F(x)= x³ - x² - 9x + 9

A)x = 0,3
B)x = 1,-3
C)x = 0,-3
D)x = 1,3
E)x = 1,±3

Question 31

Find the difference quotient and simplify your answer.
F(x)= x² - x + 1, $\frac { f ( 6 + h ) - f ( 6 ) } { h }$ ,h ? 0

A) $\frac { f ( 6 + h ) - f ( 6 ) } { h } = h + 11$ ,h ? 0
B) $\frac { f ( 6 + h ) - f ( 6 ) } { h } = h + 15$ ,h ? 0
C) $\frac { f ( 6 + h ) - f ( 6 ) } { h } = h + 14$ ,h ? 0
D) $\frac { f ( 6 + h ) - f ( 6 ) } { h } = h + 12$ ,h ? 0
E) $\frac { f ( 6 + h ) - f ( 6 ) } { h } = h + 13$ ,h ? 0

Question 32

Find the domain of the function. $$f ( x ) = \frac { x - 4 } { \sqrt { x } }$$

A)Non-negative real numbers x except x = 4
B)All real numbers x except x = 0
C)Non-negative real numbers x
D)All real numbers x
E)All real numbers x such that x > 0

Question 33

Which equation does not represent y as a function of x

A)2x = 8y
B)-4y = -8
C)5x² + 5y = 3
D)3x + 6y = -5
E)7y² + 8x = 9

Question 34

Does the table describe a function? Input value
$$\begin{array} { | l | l | l | l | l | l | } \hline \text { Input value } & 5 & 10 & 14 & 10 & 5 \\\hline \text { Output value } & - 13 & - 8 & 0 & 8 & 13 \\\hline\end{array}$$

A)Yes
B)No

Question 35

Does the table describe a function? Input value
$$\begin{array} { | l | l | l | l | l | l | } \hline \text { Input value } & 2001 & 2002 & 2003 & 2004 & 2005 \\\hline \text { Output value } & 20 & 50 & 20 & 40 & 30 \\\hline\end{array}$$

A)No
B)Yes

Question 36

Find the domain of the function. $$f ( x ) = \frac { \sqrt { x + 4 } } { 4 + x }$$

A)Non-negative real numbers x
B)All real numbers x
C)All real numbers x such that x > -4
D)Non-negative real numbers x except x =4
E)All real numbers x such that x < 4

Question 37

Which equation does not represent y as a function of x

A) $y = \sqrt { 6 + 3 x }$
B)y = |-2 + 7x²|
C)x = -6y - 2
D)x = -8
E)y = -3x + 5

Question 38

Which set of ordered pairs represents a function from P to Q? P = {5,10,15,20} Q = {-1,1,3}

A){(5,3), (15,1), (5,-1), (15,3)}
B){(15,-1), (15,1), (15,3)}
C){(5,-1), (10,1), (10,3), (15,1), (20,-1)}
D){(15,1), (10,-1), (5,1), (10,3), (15,-1)}
E){(5,-1), (10,1), (15,3), (20,-1)}

Question 39

Does the table describe a function? Input value
$$\begin{array} { | l | l | l | l | l | l | } \hline \text { Input value } & 20 & 40 & 20 & 30 & 50 \\\hline \text { Output value } & 2001 & 2002 & 2003 & 2004 & 2005 \\\hline\end{array}$$

A)Yes
B)No

Question 40

Find all real values of x such that f(x)= 0. $$f ( x ) = \frac { 81 - x ^ { 2 } } { 3 }$$

A)x = ±12
B)x = ±13
C)x = ±11
D)x = ±10
E)x = ±9

Question 41

Find the value(s)of x for which f (x)= g (x). f(x)= x² + x - 13 g(x)= -5x + 3

A)x= -8,2
B)x= 8,-2
C)x= -13,1, $\frac { 3 } { 5 }$
D)x= -13,-14, $\frac { 3 } { 5 }$
E)x= 12, $\frac { 3 } { 5 }$

Question 42

Find the domain of the function. $f ( w ) = \frac { 8 w } { w + 6 }$

A)w = -6,w = 0
B)w = -6
C)all real numbers w ? -6,w ? 0
D)all real numbers
E)all real numbers w ? -6

Question 43

Find all real values of x such that f(x)= 0. $f ( x ) = \frac { 5 x - 7 } { 3 }$

A)x = 2
B)x = $\frac { 8 } { 5 }$
C)x = $\frac{9}{5}$
D)x = $\frac { 7 } { 5 }$
E)x = $\frac { 11 } { 5 }$

Question 44

Let the function f be defined by the equation y = f (x),where x and f (x)are real numbers.Find the domain and range of the function $f ( x ) = \sqrt { 25 x ^ { 2 } - 3 }$ .

A)domain: $\left( - \infty , - \frac { 3 } { 25 } \right)$
B)domain: $\left( - \frac { 3 } { 5 } , \frac { 3 } { 5 } \right)$
C)domain: $\left( - \infty , - \frac { 3 } { 25 } \right] \cup \left[ \frac { 3 } { 25 } , + \infty \right)$
D)domain: $\left( \frac { \sqrt { 3 } } { 5 } , + \infty \right)$
E)domain: $\left( - \infty , - \frac { \sqrt { 3 } } { 5 } \right] \cup \left[ \frac { \sqrt { 3 } } { 5 } , + \infty \right)$

Question 45

Evaluate the difference quotient for the function.
F (x)= 2x - 7

A)-7
B) $\frac { 7 } { 2 }$
C)7
D)2x + 7
E)2

Question 46

Evaluate the function at the specified value of the independent variable and simplify. q(p)= -6p - 3
Q(-2.6)

A)q(-2.6)= 15.6p + 18
B)q(-2.6)= 18.6
C)q(-2.6)= 12.6
D)q(-2.6)= -2.6p - 3
E)q(-2.6)= -2.6p + 3

Question 47

Find the domain of the function. $g ( p ) = \sqrt { 81 - p ^ { 2 } }$

A)-9 ? p ?9
B)p ? -9 or p? 9
C)p ? 0
D)p ? 9
E)all real numbers

Question 48

Evaluate the function at the specified value of the independent variable and simplify. $f ( p ) = \frac { - 8 p } { 9 p + 8 }$ f(y - 5)

A) f(y - 5)= $\frac { - 8 y + 40 } { 9 y - 37 }$
B) f(y - 5)= $\frac { - 8 y - 40 } { 9 y - 37 }$
C) f(y - 5)= $\frac { - 8 p + 40 } { 9 p - 37 }$
D) f(y - 5)= $- \frac { 40 } { 53 }$
E)f(y - 5)= $- \frac { 40 } { 37 }$

Question 49

Let the function $f$ be defined by the equation $y = f ( x )$ ,where $x$ and $f ( x )$ are real numbers.Find the domain of the function $f ( x ) = \sqrt { 6 x ^ { 2 } + 16 }$

A)domain: $\left( - \infty , - \frac { 16 } { 36 } \right) \cup \left( \frac { 16 } { 36 } , + \infty \right)$
B)domain: $\left( - \infty , - \frac { \sqrt { 16 } } { 6 } \right)$
C)domain: $\left( \frac { 16 } { 36 } , + \infty \right)$
D)domain: $\left( - \frac { \sqrt { 16 } } { 6 } , \frac { \sqrt { 16 } } { 6 } \right)$
E)domain: $\left( - \infty , - \frac { \sqrt { 16 } } { 6 } \right] \cup \left[ \frac { \sqrt { 16 } } { 6 } , + \infty \right)$

Question 50

Find the graph of the equation.
F (x)= | x - 4 |

A)
B)
C)
D)

Question 51

Evaluate the function at the specified value of the independent variable and simplify. $g ( w ) = \left\{ \begin{array} { c } - w , w \leq - 1 \\- w ^ { 2 } + 2 w , - 1 < w \leq 1 \\- w ^ { 3 } + 2 w ^ { 3 } , w > 1\end{array} \right.$ g( $- \frac { 1 } { 2 }$ )

A)g( $- \frac { 1 } { 2 }$ )= $\frac { 1 } { 2 }$
B)g( $- \frac { 1 } { 2 }$ )= $\frac { 5 } { 8 }$
C)g( $- \frac { 1 } { 2 }$ )= $- \frac { 7 } { 4 }$
D)g( $- \frac { 1 } { 2 }$ )= 5
E)g( $- \frac { 1 } { 2 }$ )= $- \frac { 5 } { 4 }$

Question 52

Find the difference quotient and simplify your answer.
F(y)= 6y² - 3y, $\frac { f ( 2 + h ) - f ( 2 ) } { h }$ ,h ? 0

A) $\frac { f ( 2 + h ) - f ( 2 ) } { h } = 21 + 6 h$
B) $\frac { f ( 2 + h ) - f ( 2 ) } { h } = - 3 + 6 y - \frac { 12 } { y }$
C) $\frac { f ( 2 + h ) - f ( 2 ) } { h } = - 3 + 6 h$
D) $\frac { f ( 2 + h ) - f ( 2 ) } { h } = 21 + 6 y - \frac { 12 } { y }$
E) $\frac { f ( 2 + h ) - f ( 2 ) } { h } = 1 + h$

Question 53

Find all real value of x such that f (x)= 0. f(x)= 64x² - 36

A)x = ± $\frac { 4 } { 3 }$
B)x = ± $\frac { 3 } { 4 }$
C)x = - $\frac { 9 } { 16 }$
D)x = $\frac { 4 } { 3 }$
E)x = ± $\frac { 9 } { 16 }$