To solve this problem, let's break it down step by step:
1. Start with the original function:
The original function given is [tex]\( f(x) = |x| \)[/tex].
2. Horizontal shift to the right:
Shifting a function to the right by 3 units involves replacing [tex]\( x \)[/tex] with [tex]\( (x - 3) \)[/tex]. Thus, the function becomes:
[tex]\[
f(x) = |x - 3|
\][/tex]
3. Vertical stretch by a factor of 4:
Vertical stretch by a factor of 4 involves multiplying the entire function by 4. Therefore, the vertically stretched function will be:
[tex]\[
g(x) = 4 \cdot |x - 3|
\][/tex]
4. Combine the transformations:
Combining both transformations, the rightward shift and vertical stretch, the final transformed function is:
[tex]\[
g(x) = 4|x - 3|
\][/tex]
So, the correct function describing the transformed graph is [tex]\( g(x) = 4|x - 3| \)[/tex].
Thus, the correct answer is:
A. [tex]\( g(x) = 4|x-3| \)[/tex]
