Quiz about Cubic and Absolute Value Functions Review

Question 1

Which function is graphed?

Accepted Answer

f(x) = |x + 2| - 4

Answer

f(x) = 2|x + 2| -4

Answer

f(x) = 2|x - 4| + 2

Answer

f(x) = -2|x - 4|

Question 2

Which function is graphed?

Accepted Answer

f(x) = |x - 5|

Answer

f(x) = 2|x - 5|

Answer

f(x) = |x - 5| + 5

Answer

f(x) = |x| + 5

Question 3

Describe the transformation from the Absolute Value Parent Function.

Accepted Answer

Shift up 4 units

Answer

Shift down 4 units

Answer

Shift left 4 units

Answer

Shift right 4 units

Question 4

What is the range of the absolute value function?

Accepted Answer

$$\left[0,\infty\right)$$

Answer

$$\left(-\infty,\ \infty\right)$$

Answer

$$\left[3,\ \infty\right)$$

Answer

$$\left(-\infty,\ 3\right]$$ (-infinity, 3]

Question 5

What is the equation of the graph below?

Accepted Answer

$$f\left(x\right)=\left|x-2\right|$$

Answer

$$f\left(x\right)=\left|x+2\right|$$

Answer

$$f\left(x\right)=\left|x+2\right|+2$$

Answer

$$f\left(x\right)=\left|x-2\right|+2$$

Question 6

Describe the transformation of the equation below from the parent function of f(x) = IxI to $$g\left(x\right)=\left|x+2\right|-5$$

Accepted Answer

Left 2 down 5

Answer

Left 2 up 5

Answer

Right 2 up 5

Answer

Right 2 down 5

Question 7

What translations have occurred?

Accepted Answer

right 1, up 5

Answer

left 1, up 5

Answer

left 1, down 5

Answer

right 1, down 5

Question 8

Which of the following describes the horizontal and vertical translations of the following functions:
f(x) = |x + 4| - 9

Accepted Answer

Left 4
Down 9

Answer

Left 4
up 9

Answer

Right 4
up 9

Answer

Right 4
Down 9

Question 9

What is the vertex of the following function? (Try not to graph) $$f\left(x\right)=-4\left|x+2\right|+5$$

Accepted Answer

Answer

Answer

Answer

Question 10

What is the vertex of the following function? (Try not to graph)

$$f\left(x\right)=4\left|x-3\right|+1$$

Accepted Answer

Answer

Answer

Answer

Question 11

What is the vertex of the absolute value function?

Accepted Answer

(0, 4)

Answer

(4, 0)

Answer

$$\left(-\infty,\infty\right)$$

Answer

Question 12

What is the domain of the absolute value function?

Accepted Answer

$$\left(-\infty,\infty\right)$$

Answer

(4, 0)

Answer

(0, 4)

Answer

$$\left[4,\ \infty\right)$$

Question 13

$$f\left(x\right)=\left|x-2\right|+4$$ was translated 5 units right and 1 unit down. What is the new function rule?

Accepted Answer

$$f\left(x\right)=\left|x-7\right|+3$$

Answer

$$f\left(x\right)=\left|x-7\right|+5$$

Answer

$$f\left(x\right)=\left|x+3\right|+3$$

Answer

$$f\left(x\right)=\left|x+3\right|+5$$

Question 14

Is the vertex a minimum or maximum?

Accepted Answer

maximum

Answer

minimum

Question 15

What is the y-intercept?

Accepted Answer

(0,3)

Answer

(3,0)

Answer

(0,-5)

Answer

(-5,0)

Question 16

Is the vertex a minimum or maximum?

Accepted Answer

minimum

Answer

maximum

Question 17

Write the inequality for the absolute function.

Accepted Answer

$$f\left(x\right)<-\left|x-2\right|+3$$

Answer

$$f\left(x\right)<\left|-\left(x-2\right)\right|+3$$

Answer

$$f\left(x\right)\le-\left|x-3\right|+2$$

Answer

$$f\left(x\right)>-\left|x-2\right|+3$$

Question 18

Write the inequality for the absolute value function.

Accepted Answer

$$f\left(x\right)\ge\left|x+4\right|-1$$

Answer

$$f\left(x\right)\le\left|x+4\right|-1$$

Answer

$$f\left(x\right)\ge\left|x-4\right|-1$$

Question 19

Given $$f\left(x\right)=\left|x+5\right|-2$$ Find the minimum and maximum on interval $$\left[-7,\ -2\right]$$ Use Desmos to view the graph and table.

Accepted Answer

Min: -2
Max: 1

Answer

Min: -7
Max: -2

Answer

Min: 0
Max: 1

Answer

Min: -3
Max: 2

Question 20

Determine the minimum and maximum on interval [-4, 0]

Accepted Answer

Min: 4
Max: 7

Answer

Min: 7
Max: 4

Answer

Min: 4
Max: 5

Answer

Min: -4
Max: 0

Question 21

What are the x-intercepts?

Accepted Answer

(-2, 0) and (0,0)

Answer

There are none.

Answer

All real numbers

Answer

(0, -2) and (0, 0)

Question 22

What is the y-intercept?

Accepted Answer

(0, 3)

Answer

(3, 0)

Answer

x = -1

Answer

(-5, 0) and (3, 0)

Question 23

$$f\left(x\right)=-\left|x+3\right|-4$$ was translated 6 units left and 2 units up. What is the new function rule?

Accepted Answer

$$f\left(x\right)=-\left|x+9\right|-2$$

Answer

$$f\left(x\right)=-\left|x+9\right|+2$$

Answer

$$f\left(x\right)=-\left|x-3\right|-2$$

Answer

$$f\left(x\right)=-\left|x-3\right|-6$$

Question 24

What is the axis of symmetry?

Accepted Answer

x = -1

Answer

y= -1

Answer

y = 4

Answer

x = 4

Question 25

Which equation describes a reflection across the x-axis, a translation of 7 units right and 5 units down?

Accepted Answer

$$f\left(x\right)=-\left|x-7\right|-5$$

Answer

$$f\left(x\right)=-\left|x+7\right|-5$$

Answer

$$f\left(x\right)=\left|x-7\right|-5$$

Answer

$$f\left(x\right)=-\left|x-5\right|-7$$

Question 26

What is the minimum on interval [-2, 3]?

Accepted Answer

min: -4

Answer

min: -2

Answer

min: 3

Answer

min: 1

Question 27

Which of the following functions has a line of symmetry at x = -2?

Accepted Answer

$$f(x)=|x+2|$$

Answer

$$f(x)=|x|+2$$

Answer

$$f(x)=|x-2|$$

Answer

$$f(x)=|x|-2$$

Question 28

What is the range of the function $$h(x)=-2|x+10|-7$$ ?

Accepted Answer

$$(-∞,-7]$$

Answer

$$[-10,∞)$$

Answer

$$[10,\ ∞)$$

Answer

$$[-7,∞)$$

Question 29

Determine the vertex of the function

Accepted Answer

(-2, 5)

Answer

(-2, -5)

Answer

(2, 5)

Answer

(2, -5)

Question 30

What is the vertex of the function?

f)x) = -2 |x + 3| - 2

Accepted Answer

(-3, -2)

Answer

(3, -2)

Answer

(3, 2)

Answer

(-3, 2)

Question 31

Select all that apply. (May have more than one correct answer)

f(x) = |x - 6| + 2

Accepted Answer

Horizontal translation right 6 units

Accepted Answer

Vertical translation up 2 units

Answer

Horizontal translation left 6 units

Answer

Vertical translation down 2 units

Question 32

What is the vertex of the following function?
y= 4|x|+1

Accepted Answer

(0,1)

Answer

(4,1)

Answer

(-4,1)

Answer

(4,-1)

Question 33

Identify the characteristics of the graph of

$$f\left(x\right)=\ 3\left|x+2\right|-5$$
Check all that apply.

Accepted Answer

Vertical Stretch of 3

Accepted Answer

Accepted Answer

Answer

Vertical Shrink of 3

Answer

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Question 34

Question 34.

Accepted Answer

y< -|x|+3

Answer

y< -|x-3|

Answer

y<-|x+3|

Answer

y<-3|x|

Question 35

Write the equation

Accepted Answer

y<|x+1|+4

Answer

y<|x+4|+1

Answer

y<|x-1|+4

Answer

y<|x-1|-4

Question 36

Determine the transformation

Accepted Answer

Stretch by factor of 2, right 3

Answer

Stretch by factor of 2, left 3

Answer

Shrink by factor of 2, left 3

Answer

Shrink by factor of 2, right 3

Question 37

Which function is graphed?

Accepted Answer

f(x) = -3|x - 1| + 4

Answer

f(x) = -|x - 1| + 4

Answer

f(x) = -5|x + 1| + 4

Answer

f(x) = -3|x - 4| + 1

Question 38

Write an absolute value function given the following transformations:
Vertical Stretch of 2
Horizontal shift left 1 unit
Vertical shift down 9 units

Accepted Answer

f(x) = 2|x + 1| - 9

Answer

f(x) = |2x + 1| - 9

Answer

f(x) = |2x - 1| - 9

Answer

f(x) = 2|x - 1| - 9

Question 39

Choose all functions that show a reflection over the y-axis

Accepted Answer

$$f\left(x\right)=\left|-\left(x+5\right)\right|$$

Accepted Answer

$$f\left(x\right)=\left|-\left(x-1\right)\right|-4$$

Answer

$$f\left(x\right)=-\left|x\right|+5$$

Answer

$$f\left(x\right)=-\left|x+8\right|$$

Answer

$$f\left(x\right)=\left|x-6\right|-2$$

Cubic and Absolute Value Functions Review

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