5.2 Quiz Review
Name: ______________________________
Date: ________________ Period:______
1. Choose True or False for each statement about the function f ( x)   x 7 .
A. The function is even.
True
False
B. The domain of the function is  0,  
True
C. The range of the function is  ,  
True
False
D. As x  , f ( x)  
True
False
False
2. Choose True or False for each statement about the function f ( x)  x 20 .
A. The function is odd.
True
False
B. The domain of the function is  ,  
True
C. The range of the function is  ,0
True
False
D. As x  , f ( x)  
True
False
For 3-6, determine the number of turning points and the number and type (global or local) of any
maximum or minimum values.
a. f ( x )  x( x  2)( x  1)
4. f ( x )  ( x  1)3 ( x  1)
Turning points: _______________
Turning points: _______________
Maximum: _________________________
Maximum: _________________________
Minimum: __________________________
Minimum: __________________________
5. 𝑓(𝑥) = 𝑥 3 (𝑥 − 5)(𝑥 + 3)
6. 𝑓(𝑥) = 𝑥 4 (𝑥 + 1)3 (𝑥 + 4)
Turning points: _______________
Turning points: _______________
Maximum: _________________________
Maximum: _________________________
Minimum: __________________________
Minimum: __________________________
False
For 7-8, Graph the function. State the end behavior, x-intercepts, and intervals where the function is
above or below the x-axis.
7.
f ( x)   x 2 ( x  1)( x  2)
8. f ( x)   x  2 x  3 x  1
End behavior: _______________________
End behavior: _______________________
_______________________
_______________________
x-intercepts: ________________________
x-intercepts: ________________________
Above x-axis: ________________________
Above x-axis:________________________
Below x-axis: ________________________
Below x-axis:________________________
9. To create an open-top box out of a sheet of cardboard that is 6
inches long and 4 inches wide, you make a square flap of side
length x inches in each corner by cutting along one of the
flap's sides and folding along the other. (In the diagram, a solid
line segment in the interior of the rectangle indicates a cut,
while a dashed line segment indicates a fold.) Once you fold
up the four sides of the box, you glue each flap to the side it
overlaps. To the nearest tenth, find the value of x that
maximizes the volume of the box.
10. To create an open-top box out of a sheet of cardboard that is 8 inches long and 5 inches wide, you make a
square flap of side length x inches in each corner by cutting along one of the flap’s sides and folding along
the other. Once you fold up the four sides of the box, you glue each flap to the side it overlaps. To the
nearest tenth, find the value of x that maximizes the volume of the box.
11. Write a cubic function in intercept form for the given graph, whose x-intercepts are integers. Assume that
the constant factor a is either 1 or -1.
Equation: ________________________
12. Write a quartic function in intercept form for the given graph, whose x-intercepts are integers. Assume that
the constant factor a is either 1 or -1.
Equation: ________________________