Question

The functions f(x) and g(x) are described using the following equation and table:f(x) = −3(1.02)^xxg(x)−1−50−31−121Which statement best compares the y-intercepts of f(x) and g(x)? The y-intercept of f(x) is equal to the y-intercept of g(x). The y-intercept of f(x) is equal to 2 times the y-intercept of g(x). The y-intercept of g(x) is equal to 2 times the y-intercept of f(x). The y-intercept of g(x) is equal to 2 plus the y-intercept of f(x).

Answer 1

1st option: The y-intercept of f(x) is equal to the y-intercept of g(x).

Explanation:

The y-intercept can be determined when x = 0, therefore:

For f(x):

`\begin{gathered} f\mleft(0\mright)=-3\mleft(1.02\mright)^0 \\ f(0)=-3\cdot1 \\ f(0)=-3 \\ \text{the y-intercept is (0, -3)} \end{gathered}`

In the function g(x), we can see that when x = 3, g(x) = -3, which means that the y-intercept is (0,-3)

Which means that the intercept is the same for both functions.

The correct answer then would be:

The y-intercept of f(x) is equal to the y-intercept of g(x).