Question

Which of the following is a key property of the absolute value parent function? A. It is U-shaped. B. Its vertex is at the origin. C. It has a slope of 1 on the left half. D. It is in quadrants III and IV.

Answer 1

The absolute value parent function has a U-shaped graph with its vertex at the origin, lying in quadrants I and II.

Step-by-step explanation:

The key property of the absolute value parent function being discussed is its graphical representation. Absolute value functions are indeed U-shaped, as the function f(x) = |x| creates a V-shape graph with its vertex at the origin (0,0). This graph branches out with a slope of 1 in the positive direction (right half) and a slope of -1 in the negative direction (left half). Therefore, it is incorrect to say that it has a slope of 1 on the left half. The graph of an absolute value function lies in quadrants I and II, not in quadrants III and IV.

So considering the options, the most accurate choice would be:

B. Its vertex is at the origin.