Question

A function g(x) has x-intercepts at (1/2, 0) and (6, 0). which could be g(x)?

A. g(x) = 2(x + 1)(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

I believe the answer is B.

Answer 2

The x-intercepts of a function are used to express the function into factored form:
From (1/2, 0)
(x - 1/2)

From (6, 0)
(x-6)

(x - 1/2) (x-6) = 0
(2x -1)(x-6) = 0

The function is:
B. g(x) = (x – 6)(2x – 1)