Which of the following are characteristics of the graph of the absolute value parent function?Check all that apply.A.It goes through the origin.B.The right half has a slope of 1.C.The left half has a slope of −1.D.It is in quadrants II and IV.
Question
Which of the following are characteristics of the graph of the absolute value parent function?Check all that apply.A.It goes through the origin.B.The right half has a slope of 1.C.The left half has a slope of −1.D.It is in quadrants II and IV.
Solution
The characteristics of the graph of the absolute value parent function are:
A. It goes through the origin. This is true because the absolute value of 0 is 0, so the graph intersects the origin (0,0).
B. The right half has a slope of 1. This is true because for every positive x, the y value is also x, which means the slope is 1.
C. The left half has a slope of -1. This is true because for every negative x, the y value is -x, which means the slope is -1.
D. It is in quadrants II and IV. This is false. The graph of the absolute value function is in quadrants I and II. The graph is not in quadrant IV because the y-values of the absolute value function are never negative.
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