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Select the correct answer.

Consider the two functions given below.

f(x)=-3x-5
g(x)=f(x)+9

What is the y-intercept of g?

A.
(0,-5)
B.
(0,9)
C.
(0,4)
D.
(0,14)

1 answer

To find the y-intercept of the function \( g(x) \), we first need to express it in terms of \( x \).

Given:

  1. \( f(x) = -3x - 5 \)
  2. \( g(x) = f(x) + 9 \)

Substituting \( f(x) \) into the equation for \( g(x) \):

\[ g(x) = (-3x - 5) + 9 \]

Now, simplify \( g(x) \):

\[ g(x) = -3x - 5 + 9 \] \[ g(x) = -3x + 4 \]

Now, to find the y-intercept of \( g(x) \), we set \( x = 0 \):

\[ g(0) = -3(0) + 4 = 4 \]

Thus, the y-intercept of \( g(x) \) is \( (0, 4) \).

The correct answer is:

C. (0, 4)