Question

Which of the following are characteristics of the graph of the absolute value parent function?

Check all that apply.

A. The left half has a slope of −1.
B. The right half has a slope of 1.
C. It is in quadrants II and IV.
D. It goes through the origin.

Answer 1

The correct answer for the given question above would be all but C. The characteristics of the graph of the absolute value parent function are the following: The left half has a slope of −1; The right half has a slope of 1 and it goes through the origin. Hope this answers your question. Have a great day!

Answer 2

The graph of an absolute value parent function is a pair of rays in quadrant 1 & 2, as shown in the graph.

The absolute value function is

f(x) = |x| or y = |x|

We also know that the absolute function can be wriiten as

y = |x|

=> y = x or y = -x

Comparing with y = mx + c

We get

m = 1 or m=-1 and c = 0

c = 0 implies that the line passes through the origin.

Hence the slopes shall be -1, 1 & the line passes through the origin.

Option A, B & D are the right answers.