Q: Which of the following is the correct piecewise definition of the absolute value function $$y = |x|$$?

$$y = \begin{cases} x, & x \geq 0 \\ -x, & x \u003c 0 \end{cases}$$

Question 1

Which of the following best describes the domain and range of the absolute value function $$y = |x|$$?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$[0, \infty)$$

Question 2

Given the function $$y = |x|$$, what is the value of $$y$$ when $$x = -3$$?

Accepted Answer

$$3$$

Question 3

Which graph represents the absolute value function $$y = |x|$$?

Accepted Answer

A V-shaped graph opening upwards with vertex at $$(0,0)$$

Question 4

If $$y = |x|$$, which of the following statements is true about the symmetry of the graph?

Accepted Answer

The graph is symmetric about the $$y-$$axis

Question 5

A company charges a delivery fee based on the absolute value function $$f(x) = |x|$$, where $$x is $$the distance in miles from the warehouse. If a customer lives 5 miles away, what is the delivery fee?

Accepted Answer

$$5$$

Question 6

Which of the following is the correct piecewise definition of the absolute value function $$y = |x|$$?

Accepted Answer

$$y = \begin{cases} x, & x \geq 0 \ -x, & x \u003c 0 \end{cases}$$

Question 7

For the function $$y = |x|$$, which of the following points lies on its graph?

Accepted Answer

$$(2, 2)$$

Question 8

If the graph of $$y = |x| is $$shifted 3 units up, what is the new equation?

Accepted Answer

$$y = |x| + 3$$

Question 9

Which of the following best describes the range of the function $$y = |x|$$?

Accepted Answer

$$[0, \infty)$$

Question 10

A temperature sensor records the difference between the current temperature and a set point using $$y = |x|. If $$the set point is $$20^\circC $$and the current temperature is $$16^\circC$$, what does the sensor display?

Accepted Answer

$$4$$

Question 11

Which transformation will result in the graph of $$y = |x|$$ being reflected over the $$x-$$axis?

Accepted Answer

$$y = -|x|$$

Question 12

If $$y = |x|$$, what is the slope of the graph for $$x \u003e 0$$?

Accepted Answer

$$1$$

Question 13

Which of the following statements is true about the vertex of the graph $$y = |x|$$?

Accepted Answer

The vertex is at $$(0, 0)$$

Question 14

If $$y = |x|$$ models the distance from a point to the origin on a number line, what is the distance from $$-7 to $$the origin?

Accepted Answer

$$7$$

Question 15

Which of the following is NOT a property of the absolute value function $$y = |x|$$?

Accepted Answer

It is differentiable everywhere

Key Parent Functions: Cubic and Absolute Value Functions

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