Question

The function f(x) = (x + 5)(2 – 3) is dilated by a to produce the function g(x) = 2 · f(2).

How many c-intercepts does the function g(x) have?

A) 1
B) 2
C) 0
D) 3

Answer 1

The c-intercepts of a function are the points where the graph crosses the x-axis. Since g(x) is a constant function with a value of -14, it does not cross the x-axis, hence it has 0 c-intercepts.

Step-by-step explanation:

The student needs to determine the number of c-intercepts for the given function g(x). The original function is f(x) = (x + 5)(2 - 3), which simplifies to f(x) = -(x + 5). The function g(x) is a dilation by a factor of 2 at x-value 2; hence g(x) = 2 · f(2) = 2 · [-(2 + 5)] = 2 · -7 = -14. Therefore, g(x) is a constant function and does not have any x-intercept. The c-intercepts, which are essentially the x-intercepts, are the points where the graph of the function crosses the x-axis. Since g(x) is a horizontal line with a constant output of -14, it does not cross the x-axis at all. Thus, there are no c-intercepts, and the correct answer is C) 0.