4. the functions $f$ and $g$ are given by $f(x)=cos(x)$ and $g(x)=cos(5x)$. how are the graphs of $f$ and…
4. the functions $f$ and $g$ are given by $f(x)=cos(x)$ and $g(x)=cos(5x)$. how are the graphs of $f$ and $g$ related?
Answer
Answer:
The graph of $g(x)=\cos(5x)$ is a horizontal compression of the graph of $f(x)=\cos(x)$ by a factor of $\frac{1}{5}$.
Explanation:
Step1: Recall transformation rule
For $y = f(bx)$ where $b>1$, graph is compressed horizontally.
Step2: Identify $b$ value
In $g(x)=\cos(5x)$ and $f(x)=\cos(x)$, $b = 5$.
Step3: Determine compression factor
The compression factor is $\frac{1}{b}=\frac{1}{5}$.