Question

A function g(x) has x-intercepts at (-3, 0) and (6, 0). Which could be g(x)?

A. g(x) = 2(x + 3)(x - 6)

B. g(x) = (x - 6)(2x - 1)

C. g(x) = 2(x - 2)(x - 6)

D. g(x) = (x + 6)(x + 2)

Answer 1

To find the function g(x) with x-intercepts at (-3, 0) and (6, 0), we evaluate each option. Option A, g(x) = 2(x + 3)(x - 6), satisfies the conditions.

Step-by-step explanation:

To find the function g(x) that has x-intercepts at (-3, 0) and (6, 0), we need to check which option satisfies these conditions. Let's evaluate each option:

A. g(x) = 2(x + 3)(x - 6) - When x = -3 or x = 6, the expression is equal to zero. So, this option could represent g(x).

B. g(x) = (x - 6)(2x - 1) - When x = -3 or x = 6, the expression is not equal to zero. So, this option could not represent g(x).

C. g(x) = 2(x - 2)(x - 6) - When x = -3 or x = 6, the expression is not equal to zero. So, this option could not represent g(x).

D. g(x) = (x + 6)(x + 2) - When x = -3 or x = 6, the expression is not equal to zero. So, this option could not represent g(x).

Based on the above analysis, option A - g(x) = 2(x + 3)(x - 6) - could be g(x).