Questions: Given (f(x)=x^2-4). - Use stretching and shrinking of (f(x)) to write the equation of (h(x)). - Be sure to check your equation by graphing (f(x)) and (h(x)) in the same graphing window, and revise your equation for (h(x)) if necessary. - Select the appropriate equation for (h(x)) from the list of options below. (h(x)=frac14 f(x)) (h(x)=fleft(frac12 xright)) (h(x)=4 f(h)) (h(x)=f(4 x))

$Given (f(x)=x^2-4). - Use stretching and shrinking of (f(x)) to write the equation of (h(x)). - Be sure to check your equation by graphing (f(x)) and (h(x)) in the same graphing window, and revise your equation for (h(x)) if necessary. - Select the appropriate equation for (h(x)) from the list of options below. (h(x)=frac14 f(x)) (h(x)=fleft(frac12 xright)) (h(x)=4 f(h)) (h(x)=f(4 x))$

Transcript text: - Given $f(x)=x^{2}-4$. - Use stretching and shrinking of $f(x)$ to write the equation of $h(x)$. - Be sure to check your equation by graphing $f(x)$ and $h(x)$ in the same graphing window, and revise your equation for $h(x)$ if necessary. - Select the appropriate equation for $h(x)$ from the list of options below. $h(x)=\frac{1}{4} f(x)$ $h(x)=f\left(\frac{1}{2} x\right)$ $h(x)=4 f(h)$ $h(x)=f(4 x)$

Solution

Solution Steps

Step 1: Identify the given function

The given function is $ f(x) = x^2 - 4 $.

Step 2: Analyze the transformation

We need to determine how $ f(x) $ is transformed to become $ h(x) $. By comparing the graphs, we can see that $ h(x) $ is a horizontally stretched version of $ f(x) $.

Step 3: Determine the transformation factor

The graph of $ h(x) $ is wider than $ f(x) $. This indicates a horizontal stretch. A horizontal stretch by a factor of $ k $ is represented by $ h(x) = f\left(\frac{x}{k}\right) $. By examining the graph, we can see that $ h(x) $ is stretched by a factor of 2.