what kind of transformation converts the graph of f(x) = x² + 4 into the graph of g(x) = 9x² + 4? horizontal…

Explanation:

Step1: Recall transformation rules

For a function $y = f(x)$, if we have $y = a\cdot f(x)$ ($a>1$), it's a vertical stretch; if $0 < a< 1$, it's a vertical shrink. If we have $y = f(bx)$ ($b > 1$), it's a horizontal shrink and if $0 < b<1$, it's a horizontal stretch. Given $f(x)=x^{2}+4$ and $g(x)=9x^{2}+4 = f(3x)$.

Step2: Identify the transformation

Here, we can rewrite $g(x)$ as $f(3x)$ where the $x$ - value in $f(x)$ is being multiplied by 3. According to the rules of function - transformations, when we change $f(x)$ to $f(bx)$ with $b = 3>1$, it represents a horizontal shrink.

Answer:

horizontal shrink