Let g(x) be the indicated transformation(s) of f (x) = x. Write the rule for g(x) .15. vertical stretch by a factor of 4

Step 1: Break Down the Problem

We need to identify the transformations applied to the function $f(x) = x$. In this case, we are performing a vertical stretch by a factor of 4 on the function.

Step 2: Relevant Concepts

A vertical stretch by a factor of $a$ on a function $f(x)$ is given by the new function $g(x) = a \cdot f(x)$. Here, since we are stretching by a factor of 4, we have:

• $a = 4$

Step 3: Analysis and Detail

Given the function $f(x) = x$, applying the vertical stretch transformation involves multiplying $f(x)$ by 4:

$g(x) = 4 \cdot f(x) = 4 \cdot x$

Step 4: Verify and Summarize

The transformation has been correctly applied by multiplying the original function by 4, which confirms that $g(x) = 4x$.

Final Answer

The rule for $g(x)$ is:

$g(x) = 4x$