Question

question 4 (multiple choice worth 2 points) (transformations of linear functions mc) given that f(x) crosses the y - axis at (0, 5) determine the y - intercept of the new function g(x) = f(x) + 4. options: 5, -3, 9

Explanation:

Step1: Recall y - intercept definition

The y - intercept of a function \(y = f(x)\) is the value of \(f(x)\) when \(x = 0\). We know that for \(f(x)\), when \(x = 0\), \(f(0)=5\) (since it crosses the y - axis at \((0,5)\)).

Step2: Find \(g(0)\)

We are given the function \(g(x)=f(x) + 4\). To find the y - intercept of \(g(x)\), we need to find \(g(0)\). Substitute \(x = 0\) into the function \(g(x)\):
\(g(0)=f(0)+4\)
We know that \(f(0) = 5\), so substitute \(f(0)\) into the equation:
\(g(0)=5 + 4=9\)

Answer:

The y - intercept of \(g(x)\) is \(9\), so the correct option (assuming the options are presented as, for example, A. 5, B. - 3, C. 9) is C. 9.