Deck 5: Analyzing Graphs of Functions

Question 1

Select the graph of the function and determine whether it is even,odd,or neither.? $$f ( x ) = \sqrt { 3 - x }$$ ?

A)? Even
B)? Odd
C)? Odd
D)? Even
E)? Neither

Answer 1

? Neither

Question 2

Select the graph of the function and find the zeros of the function.? $$f ( x ) = \sqrt { 2 x + 3 }$$ ?

A)? $$x = \frac { 2 } { 3 }$$
B)? $$x = \frac { 3 } { 2 }$$
C)? $$x = - \frac { 3 } { 2 }$$
D)? $$x = - \frac { 3 } { 2 }$$
E)? $$x = - \frac { 2 } { 3 }$$

Answer 2

? $$x = - \frac { 3 } { 2 }$$

Question 3

?Find the zeros of the function algebraically.? $$f ( x ) = 9 x ^ { 2 } + 21 x - 18$$ ?

A)? $x = \frac { 2 } { 3 } , - 3$
B)? $x = - \frac { 2 } { 3 } , - 3$
C)? $x = \frac { 3 } { 2 } , - 3$
D)? $x = \frac { 2 } { 3 } , 3$
E)? $x = - \frac { 2 } { 3 } , 3$

Answer 3

? $x = \frac { 2 } { 3 } , - 3$

Question 4

Select the graph of the function and determine whether it is even,odd,or neither. ​
F(x)= 6x - 5
​

A)​ Even
B)​ Even
C)​ Odd
D)​ Neither
E)​ Odd

Question 5

Find the zeros of the function algebraically.? $$f ( x ) = \frac { x } { 9 x ^ { 2 } - 5 }$$ ?

A)x = 5
B)x = 10
C)x = 9
D)x = 8
E)x = 0

Question 6

Find the zeros of the function algebraically.? $$f ( x ) = \sqrt { 5 x + 2 }$$ ?

A) $x = - \frac { 2 } { 5 }$
B) $x = \frac { 2 } { 5 }$
C)? $x = \frac { 5 } { 2 }$
D) $x = - \frac { 5 } { 2 }$
E) $x = - 2$

Question 7

Find the average rate of change of the function from x₁ = 1 to x₂ = 5.? $$f ( x ) = x ^ { 2 } + 18 x - 4$$ ?

A)The average rate of change from x₁ = 1 to x₂ = 5 is 24.
B)The average rate of change from x₁ = 1 to x₂ = 5 is -4.
C)The average rate of change from x₁ = 1 to x₂ = 5 is -24.
D)The average rate of change from x₁ = 1 to x₂ = 5 is -18.
E)The average rate of change from x₁ = 1 to x₂ = 5 is 4.

Question 8

?Find the zeros of the function algebraically.?? $$f ( x ) = 2 x ^ { 2 } - 9 x - 35$$

A)? $x = - \frac { 5 } { 2 } , 7$
B)? $x = - \frac { 5 } { 2 } , - 7$
C)? $x = - \frac { 2 } { 5 } , 7$
D)? $x = \frac { 5 } { 2 } , - 7$
E)? $x = \frac { 5 } { 2 } , 7$

Question 9

Select the graph of the function and determine whether it is even,odd,or neither. ​
F(x)= x² - 6
​

A)​ Odd
B)​ Neither
C)​ Odd
D)​ Neither
E)​ Even

Question 10

Find the average rate of change of the function from x₁ = 1 to x₂ = 5.? $$f ( x ) = x ^ { 2 } - 3 x + 6$$ ?

A)The average rate of change from x₁ = 1 to x₂ = 5 is 19.
B)The average rate of change from x₁ = 1 to x₂ = 5 is 3.
C)The average rate of change from x₁ = 1 to x₂ = 5 is -6.
D)The average rate of change from x₁ = 1 to x₂ = 5 is -3.
E)The average rate of change from x₁ = 1 to x₂ = 5 is 6.

Question 11

Find the average rate of change of the function from x₁ = 0 to x₂ = 3.? $$f ( x ) = - 2 x + 12$$ ?

A)The average rate of change from x₁ = 0 to x₂ = 3 is -2.
B)The average rate of change from x₁ = 0 to x₂ = 3 is 12.
C)The average rate of change from x₁ = 0 to x₂ = 3 is 2.
D)The average rate of change from x₁ = 0 to x₂ = 3 is -12.
E)The average rate of change from x₁ = 0 to x₂ = 3 is 19.

Question 12

Find the average rate of change of the function from x₁ = 1 to x₂ = 3.? $$f ( x ) = x ^ { 3 } - 8 x ^ { 2 } - x$$ ?

A)The average rate of change from x₁ = 1 to x₂ = 3 is 19.
B)The average rate of change from x₁ = 1 to x₂ = 3 is -20.
C)The average rate of change from x₁ = 1 to x₂ = 3 is 8.
D)The average rate of change from x₁ = 1 to x₂ = 3 is -14.
E)The average rate of change from x₁ = 1 to x₂ = 3 is 14.

Question 13

Find the average rate of change of the function from x₁ = 1 to x₂ = 6.? $$f ( x ) = - x ^ { 3 } + 2 x ^ { 2 } + x$$ ?

A)The average rate of change from x₁ = 1 to x₂ = 6 is 19.
B)The average rate of change from x₁ = 1 to x₂ = 6 is -9.
C)The average rate of change from x₁ = 1 to x₂ = 6 is 9.
D)The average rate of change from x₁ = 1 to x₂ = 6 is -28.
E)The average rate of change from x₁ = 1 to x₂ = 6 is -2.

Question 14

Find the average rate of change of the function from x₁ = 0 to x₂ = 3.? $$f ( x ) = 3 x + 10$$ ?

A)The average rate of change from x₁ = 0 to x₂ = 3 is -3.
B)The average rate of change from x₁ = 0 to x₂ = 3 is 3.
C)The average rate of change from x₁ = 0 to x₂ = 3 is -10.
D)The average rate of change from ?x₁ = 0 to x₂ = 3 is 10.
E)The average rate of change from x₁ = 0 to x₂ = 3 is 19.

Question 15

Select the graph of the function and determine whether it is even,odd,or neither. ​
F(x)= 4
​

A)Neither ​
B)Odd​ ​
C)Even ​
D)Even ​
​
E)Odd ​

Question 16

Select the graph of the function and find the zeros of the function.? $$f ( x ) = 7 + \frac { 13 } { x }$$ ?

A) ? $$x = - 13$$
B)? $$x = \frac { 7 } { 13 }$$
C) ? $$x = - \frac { 7 } { 13 }$$
D)? $$x = \frac { 13 } { 7 }$$
E)? $$x = - \frac { 13 } { 7 }$$

Question 17

Find the zeros of the function algebraically.? $$f ( x ) = \sqrt { 16 x } - 1$$ ?

A)x = 0,16
B) $x = \frac { 1 } { 16 }$
C) $x = 0 , \sqrt { 16 }$
D) $x = 0 , \pm \sqrt { 16 }$
E) $x = 0 , \pm 16$

Question 18

Find the zeros of the function algebraically.? $$f ( x ) = \frac { 1 } { 8 } x ^ { 3 } - x$$ ?

A) $x = 0 , \sqrt { 8 }$
B) $x = 0 , - \sqrt { 8 }$
C) $x = 0 , \pm 8$
D) $x = 0 , \pm \sqrt { 8 }$
E) $x = 0,8$

Question 19

Select the graph of the function and find the zeros of the function.? $$f ( x ) = x ( x - 6 )$$ ?

A)? ?x = 0,9
B)? ?x = -6,0
C)? ?x = -6,0
D)? x = 6
E)? x = 0,6

Question 20

?Find the zeros of the function algebraically.?? $$f ( x ) = \frac { x ^ { 2 } - 10 x + 16 } { 7 x }$$

A)? $x = - 2,0,8$
B)? $x = - 8,0,2$
C)? $x = 2,8$
D)? $x = 0,2,8$
E)? $x = - 8 , - 2,0$

Question 21

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is odd. ​
(8,-7)
​

A)(8,7)
B)(8,-7) ​
C)(-8,-7) ​
D)(-8,7) ​
E)None of the above

Question 22

Use the Vertical Line Test to determine in which of the graphs y is not a function of x. ?

A)All of the choices (A,B,C,and D)represent functions.
B)?x² + y² = 16 ?
?
C)? $$y = x ^ { 2 } + 2 x - 3$$ ?
D)? $$y = x ^ { 3 } - 2$$ ?
E)? $$y = \frac { 1 } { x }$$ ?

Question 23

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is odd. ​
(4a,6b)
​

A)​(-4a,-6b)
B)​(-4a,6b)
C)​(4a,-6b)
D)​(4a,6b)
E)None of the above

Question 24

Find the zeroes of the functions algebraically.? $$f ( x ) = \frac { x ^ { 2 } - 14 x + 48 } { 7 x }$$ ?

A) $x = - 8 , x = - 6 , x = \frac { 1 } { 7 }$
B) $x = 8 , x = 6$
C)? $$x = - 8 , x = - 6$$
D) $x = \frac { 1 } { 7 }$
E) $x = 8 , x = 6 , x = \frac { 1 } { 7 }$

Question 25

An object is thrown upward from ground level at a velocity of 90 feet per second. Use the position equation s = -16t² + v₀t + s₀ to select a function that represents the situation and select the graph of the function.
​

A)s = -16t² + 90t ​
​
B)s = -16t² - 90t ​
C)s = 16t² + 90t ​
​
D)s = 16t² - 90t ​
​
E)s = -16t² + 90t + 8 ​
​

Question 26

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is even. ​
(4,3)
​

A)(-4,-3)
B)(-4,3)
C)(4,3) ​
D)​(4,-3) ​
E)None of the above

Question 27

Select the graph of the given function and determine the interval(s)for which f(x)≥ 0. ​
F(x)= 5 - x
​

A)​ ​
(∞,-5]
B)​ ​
​(-∞,-5]
C)​ ​
​(∞,5]
D)​ ​
​(-∞,5]
E)​ ​
​​(-∞,5]

Question 28

An object is dropped from a height of 60 feet. Use the position equation s = -16t² + v₀t + s₀ to write a function that represents the situation and select the graph of the function.
​

A)s = 16t² + ​60 ​
​
B)s = -16t² - ​60 ​
​
C)s = 16t² - ​60 ​
​
D)s = -16t² + ​60 ​
​
E)s = -16t² + ​60t ​
​

Question 29

An object is thrown upward from a height of 6.4 feet at a velocity of 80 feet per second. Use the position equation s = -16t² + v₀t + s₀ to select a function that represents the situation and select the graph of the function.
​

A)s = -16t² + 80 - 6.4 ​
B)s = -16t² + 80t ​
​
C)s = -16t² - 80t - 6.4 ​
D)s = -16t² - 80t + 6.4 ​
E)s = -16t² + 80t + 6.4 ​
​

Question 30

The number of lumens (time rate of flow of light)L from a fluorescent lamp can be approximated by the model ​
L = -0.294x² + 97.744x - 664.875, 20 ≤ x ≤ 90
​
Where x is the wattage of the lamp.
​
Use a graphing utility to select the graph of the function.Use the graph to estimate the wattage necessary to obtain 2400 lumens.
​

A)​ 40W
B)​ 30W
C)​ 45W
D)​ 25W
E)​ 35W

Question 31

Select the graph of the given function and determine the interval(s)for which f(x)? 0.? $$f ( x ) = - ( 6 + | x | )$$ ?

A)? ?
F(x)> 6 for all x.
B)? ?
F(x)< 0 for all x.
C)? ?
F(x)? 0 for all x.
D)? ?
F(x)? 0 for all x.
E)? ?
F(x)> 0 for all x.

Question 32

Select the graph of the function and determine whether it is even,odd,or neither.? $$g ( t ) = \sqrt [ 3 ] { t - 4 }$$ ?

A)? Even
B)? Odd
C)? Neither
D)? Even
E)? Odd

Question 33

Select the graph of the given function and determine the interval(s)for which f(x)? 0.? $$f ( x ) = \sqrt { x - 2 }$$ ?

A)? ?
(-?,2]
B)? ?
[-2,?)
C)? ?
?[-2,2)
D)? ?
[2,?)
E)? ?
[-2,?)

Question 34

An object is dropped from a height of 15 feet. Use the position equation s = -16t² + v₀t + s₀ to write a function that represents the situation and select the graph of the function.
​

A)s = -16t² + 15t ​
​
B)s = -16t² + 15 ​
​
C)s = -16t² - 15t ​
​
D)s = 16t² + 15 ​
​
E)s = -16t² - 15 ​
​

Question 35

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is even. ​
(-x,y)
​

A)(-x,-y)
B)(x,-y)
C)(-x,y)
D)(x,y)
E)None of the above

Question 36

Select the graph of the given function and determine the interval(s)for which f(x)≥ 0. ​
F(x)= 16 - x²
​

A)​ ​
[-4,-4]
B)​ ​
[-4,4]
C)​ ​
[-4,-4]
D)​ ​
[4,-4]
E)​ ​
[-4,4]

Question 37

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is even.? $\left( - \frac { 1 } { 2 } , 5 \right)$ ?

A) $\left( - \frac { 1 } { 2 } , - 5 \right)$
B) $\left( \frac { 1 } { 2 } , 5 \right)$ ?
C) $\left( \frac { 1 } { 2 } , - 5 \right)$ ?
D) $\left( - \frac { 1 } { 2 } , 5 \right)$ ?
E)None of the above

Question 38

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is odd.? $\left( - \frac { 9 } { 7 } , - 4 \right)$ ?

A) $\left( \frac { 9 } { 7 } , 4 \right)$
B)? $\left( - \frac { 9 } { 7 } , 4 \right)$
C)? $\left( - \frac { 9 } { 7 } , - 4 \right)$
D)? $\left( \frac { 9 } { 7 } , - 4 \right)$
E)None of the above

Question 39

An object is thrown upward from a height of 8 feet at a velocity of 72 feet per second. Use the position equation s = -16t₂ + v₀t + s₀ to select a function that represents the situation and select the graph of the function.
​

A)​ s = -16t² - 72t + 8 ​
B)​ s = -16t² + 72t ​
C)​ s = -16t² + 72t - 8 ​
​
D)s = -16t² + 72t + 8 ​
E)​ s = -16t² - 72t - 8 ​

Question 40

Select the graph of the function and determine whether it is even,odd,or neither. ​
F(x)= |x + 6|
​

A)​ Even
B)​ Odd
C)​ Neither
D)​ Odd
E)​ Even

Question 41

Graph the piecewise-defined function.? $$y = f ( x ) = \left\{ \begin{array} { r } x + 6 , \text { if } x < 0 \\6 , \text { if } x \geq 0\end{array} \right.$$ ?

A)
B)
C)
D)

Question 42

The graph of the function is sketched as follows:​ ​
Determine the interval where the function is increasing.

Question 43

Tell where the function is decreasing.​ ​

A)always increasing
B)always decreasing
C)(0,∞)
D)always constant
E)(-∞,0)

Question 44

Use a graphing utility to graph the function and approximate (to two decimal places)any relative minimum or relative maximum values. $$f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 2 x + 3$$

A)relative maximum: (2.58,0.39) relative minimum: (7.27,-1.72)
B)relative maximum: (0.39,2.58) relative minimum: (-1.72,7.27)
C)relative maximum: (-1.72,7.27) relative minimum: (0.39,2.58)
D)relative maximum: (7.27,-1.72) relative minimum: (2.58,0.39)
E)relative maximum: (2.58,28.33) relative minimum: (7.27,478.41)

Question 45

Tell where the function is decreasing.? ?

A) $( 3 , \infty )$
B) $( - \infty , 3 )$
C)always increasing
D)always constant
E)always decreasing

Question 46

Determine the intervals over which the function is increasing,decreasing,or constant. $$f ( x ) = \left\{ \begin{array} { l } - x ^ { 2 } , x < 1 \\x ^ { 2 } - 2 x + 2 , x \geq 1\end{array} \right.$$

A)?constant on (-?,0) increasing on (0,?)
?
B)increasing on (-?,0), (1,?) descreasing on (0,1)
C)??constant on (-?,1) increasing on (1,?)
?
D)?constant on (-?,1) descreasing on (1,?)
?
E)?constant on (-?,0) descreasing on (0,1)
?

Question 47

Graph the function.? $$y = [ [ 4 x ] ]$$ ?

A)
B)?
C)?
D)?

Question 48

Find the zeroes of the functions algebraically.? $$f ( x ) = \sqrt { 5 x } - 9$$ ?

A) $x = \pm \frac { 9 } { 5 }$
B) $$x = \pm \frac { 81 } { 5 }$$
C)? $x = \frac { 9 } { 5 }$
D)? $x = \frac { 81 } { 5 }$
E)?no real zeroes

Question 49

Use a graphing utility to graph the function and visually determine the intervals over which the function is increasing,decreasing,or constant.? $f ( x ) = 6 x ^ { 2 } - 12 x + 6$ ?

A)?increasing on (-?,?)
B)descreasing on (-?,1) increasing on (1,?)
C)?increasing on (-?,1) descreasing on (1,?)
D)?descreasing on (-?,?)
E)descreasing on (1,1) increasing on (1,?)

Question 50

​Use the position equation s = -16t² + v₀t + s₀ to write a function that represents the situation and give the average velocity of the object from time t₁ to time t₂. An object is thrown upward from a height of 38 feet at a velocity of 84 feet per second.
T₁ = 1,t₂ = 3

A)​s = -16t² + 38t + 84;avg.velocity = 79 ft/s
B)​s = -16t² + 84t + 38;avg.velocity = 125 ft/s
C)​s = -16t² + 38t + 84;avg.velocity = -26 ft/s
D)​s = -16t² + 84t + 38;avg.velocity = 20 ft/s
E)​s = -16t² + 84t + 38;avg.velocity = 40 ft/s

Question 51

Graph the function and determine the interval(s)for which f (x)? 0. $$f ( x ) = - x ^ { 2 } - 2 x$$

A) $( - \infty , - 2 ) \cup ( 0 , \infty )$
B) $( - 2,0 )$
C) $[ - 2,0 ]$
D){-2}
E) $( - \infty , - 2 ] \cup [ 0 , \infty )$

Question 52

Determine whether the function is even,odd,or neither. ?? $$f ( x ) = 6 x ^ { 3 / 4 }$$ ?

A)neither
B)even
C)odd

Question 53

Write the height h of the rectangle as a function of x.

A)? $h ( x ) = x ^ { 2 } + 2 x$
B)? $h ( x ) = - 2 x ^ { 2 } + 8 x - 6$
C)? $h ( x ) = - 2 x ^ { 2 } + 8 x - 6$ .
D)? $h ( x ) = - 2 x ^ { 2 } + 8 x - 4$
E)? $h ( x ) = - 2 x ^ { 2 } + 6 x - 4$

Question 54

Find the graph of the equation.? $f ( x ) = \sqrt { 3 x - 4 }$ ?

A) ?
B) ?
C) ?
D) ?

Question 55

Use a graphing utility to graph the function and find the zeroes of the function.? $$f ( x ) = 7 - \frac { 3 } { x }$$ ?

A) $x = \frac { 3 } { 7 }$
B) $x = - \frac { 3 } { 7 }$
C) $x = \frac { 7 } { 3 }$
D)? $x = - \frac { 7 } { 3 }$
E)no real zeroes

Question 56

The graph of a function is sketched below.​ ​ Determine the interval on which the function is decreasing.
​

A)(-∞,-3] ∩ [-1,∞)
B)​[-3,-1]
C)​[-1,-1] ​
D)​[1,3] ​
E)(-∞,-3] ∩ [-1,∞) ​