Question

The x-intercept of f(x) is 7. If g(x) = f(x-3), then what is the x-intercept of g(x)?

a) 3
b) 4
c) 6
d) 7

Answer 1

The x-intercept of function g(x) = f(x-3) is 10, which is obtained by shifting the original function with an x-intercept at 7, to the right by 3 units. The provided multiple-choice answers do not include this correct answer, implying an error in the options given.

Step-by-step explanation:

The original function f(x) has an x-intercept at 7, which means f(7) = 0. The function g(x) = f(x-3) is a horizontal shift of the original function f(x) to the right by 3 units. Therefore, to find the x-intercept of g(x), we set g(x) to zero and solve for x:

0 = g(x) = f(x-3)

This implies that the x-intercept of the original function f(x) now occurs at x-3 = 7. So, solving for x, we get:

x - 3 = 7 → x = 10

Therefore, the correct answer is 10, which is not listed as an option in the multiple-choice answers provided. There might be a mistake in the options given, because with the information provided and the transformation applied, 10 is the x-intercept of g(x).