Question

Consider the function y = acos(bx), where a > 0 and b > 0. Which change affects the locations of the x-intercepts of the graph?

Decrease a.
Decrease b.
Change the sign of a.
Change the sign of b.

Answer 1

Answer: B

Decrease b.

Explanation:

Answer 2

The correct option is;

Decrease b.

Explanation:

The given information are;

The function in the question is given by the equation, y = a·cos(b·x)

Where;

a > 0 and b > 0

The location of the x-intercept is given by the values of x when y = 0 which are obtained as follows;

When y = 0, y = a·cos(b·x) = 0

Therefore;

cos(b·x) = 0/a = 0

∴ b·x = cos⁻¹(0) = π/2, 3·π/2, (4·n×π + π)/2

Therefore, as b decreases, x increases.