Quiz about Graphing Absolute Value Functions

Question 1

Which function is graphed? Use the general formula of absolute value function $$y=a\left|x-h\right|+k$$ where a is the slope, (h,k) is the vertex. To double check if your answer is correct, you may use desmos graphing calculator to verify which among the choices match the graph.

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? Use the general formula of absolute value function $$y=a\left|x-h\right|+k$$ where a is the slope, (h,k) is the vertex. To double check if your answer is correct, you may use desmos graphing calculator to verify which among choices match the graph.

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 3

What is the vertex of the absolute value function?

Accepted Answer

(0, 4)

Answer

(4, 0)

Answer

(-infinity, infinity)

Answer

[4, infinity)

Question 4

What is the equation of the absolute value function? Use the general formula of absolute value function $$y=a\left|x-h\right|+k$$ where a is the slope, (h,k) is the vertex. To double check if your answer is correct, you may use desmos graphing calculator to verify which among choices match the graph.

Accepted Answer

f(x)= |x| + 4

Answer

f(x)= |x+4|

Answer

f(x)= |x-4|

Answer

f(x)= |x| - 4

Question 5

What is the vertex of the following function?
y= -4|x+2|+5

Accepted Answer

(-2,5)

Answer

(-4,2)

Answer

(-4,-2)

Answer

(2,5)

Question 6

What is the equation of the graph below? You can click the picture to zoom in!

Accepted Answer

y = - | x - 2| + 4

Answer

y = - | x + 2| + 4

Answer

y = | x - 2 | + 4

Answer

y = | x - 2| - 4

Question 7

Where is the absolute value function decreasing?

Hint: There are two sides of the graph. Decreasing is the part where the line goes down or drops down from left to right.

Accepted Answer

When x < -1

Answer

When x > -1

Answer

It's never decreasing.

Answer

It's always decreasing.

Question 8

Describe the end behavior of the absolute value function shown.

Accepted Answer

$$as\ x\ \rightarrow\ \infty,\ y\ \rightarrow\ \infty$$ $$as\ x\ \rightarrow\ -\infty,\ y\ \rightarrow\ \infty$$

Answer

$$as\ x\ \rightarrow\ \infty,\ y\ \rightarrow\ -\infty$$ $$as\ x\ \rightarrow\ -\infty,\ y\ \rightarrow\ \infty$$

Answer

$$as\ x\ \rightarrow\ \infty,\ y\ \rightarrow\ -\infty$$ $$as\ x\ \rightarrow\ -\infty,\ y\ \rightarrow\ -\infty$$

Answer

$$as\ x\ \rightarrow\ -\infty,\ y\ \rightarrow\ \infty$$ $$as\ x\ \rightarrow\ -\infty,\ y\ \rightarrow\ -\infty$$

Question 9

Where is the absolute value function increasing? Hint: There are 2 sides of the graph. Increasing is the part where the line goes up from left to right.

Accepted Answer

When x < 1

Answer

When -2 < x < 4

Answer

When x < -2 & when x > 4

Answer

When x = -2 & when x = 4

Question 10

Describe the end behavior of the absolute value function shown.

Accepted Answer

$$as\ x\ \rightarrow\ \infty,\ y\ \rightarrow\ -\infty$$ $$as\ x\ \rightarrow\ -\infty,\ y\ \rightarrow\ -\infty$$

Answer

$$as\ x\ \rightarrow\ \infty,\ y\ \rightarrow\ \infty$$ $$as\ x\ \rightarrow\ -\infty,\ y\ \rightarrow\ \infty$$

Answer

$$as\ x\ \rightarrow\ \infty,\ y\ \rightarrow\ -\infty$$ $$as\ x\ \rightarrow\ -\infty,\ y\ \rightarrow\ \infty$$

Answer

$$as\ x\ \rightarrow\ \infty,\ y\ \rightarrow\ \infty$$ $$as\ x\ \rightarrow\ -\infty,\ y\ \rightarrow\ -\infty$$

Question 11

Name the parent function.

Accepted Answer

absolute value

Answer

constant

Answer

square root

Answer

linear

Question 12

What is the vertex of the absolute value function?

Accepted Answer

(0, 4)

Answer

(4, 0)

Answer

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

Answer

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

Question 13

What is the domain of the absolute value function? Hint: Graph the absolute value parent function to visualize the domain (x-values)

Accepted Answer

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

Answer

(4, 0)

Answer

(0, 4)

Answer

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

Question 14

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

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

Question 15

What is the y-intercept?

Accepted Answer

(0, 2)

Answer

(2, 0)

Answer

none

Answer

(2, 2)

Question 16

What is the axis of symmetry?

Accepted Answer

x = 15

Answer

y = 50

Answer

x = 50

Answer

y = 15

Question 17

What is/are the x-intercept(s)? Select all that apply.

Accepted Answer

(2, 0)

Accepted Answer

(-10, 0)

Answer

(0, -1)

Answer

(-4, -3)

Question 18

What is/are the x-intercept(s) of the absolute value function?

Accepted Answer

none

Answer

(0, 4)

Answer

(4, 0)

Answer

[4, infinity)

Question 19

What is the range of the absolute value function?

Accepted Answer

[0, infinity)

Answer

(-infinity, infinity)

Answer

[3, infinity)

Answer

(-infinity, 3]

Question 20

What is the maximum of the following function on the interval [-3,0]?

y= -4|x+2|+5

Accepted Answer

5

Answer

4

Answer

3

Answer

2

Question 21

The vertex is a ___________for this graph.

Accepted Answer

maximum

Answer

minimum

Question 22

What are the intercepts of this function?

f(x)= |x-5| -2

Accepted Answer

x-intercepts: (3,0) & (7,0); y-intercept (0, 3)

Answer

x-intercepts: (-5,0) & (2,0); y-intercept (0, -2)

Answer

x-intercepts: (5,0) & (-2,0); y-intercept (0, -2)

Answer

x-intercepts: (-3,0) & (7,0); y-intercept (0, 3)

Graphing Absolute Value Functions

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