Question

the power function y = ax^b is shown graphed below. which of the following must be true about the values of a and b? (1) a must be even and b must be odd (2) a must be odd and b must be negative (3) a must be positive and b must be even (4) a must be negative and b must be even

Explanation:

Step1: Analyze the symmetry of the graph

The power - function \(y = ax^{b}\) is symmetric about the y - axis. For a power function \(y = ax^{b}\), if it is symmetric about the y - axis, the function is an even function. A power function \(y = ax^{b}\) is even when \(b\) is an even integer. Also, since the graph opens downwards, the leading - coefficient \(a\) must be negative.

Answer:

(4) a must be negative and b must be even