We are given three functions: $f(x) = \frac{1}{x}$, $r(x) = x+4$, and $m(x) = 8x$. We need to find the composite function $m(f(r(x)))$. Then we have to describe how this composition transforms the parent function $f(x) = \frac{1}{x}$.

1. Problem Description

We are given three functions: $f(x) = \frac{1}{x}$, $r(x) = x+4$, and $m(x) = 8x$. We need to find the composite function $m(f(r(x)))$. Then we have to describe how this composition transforms the parent function $f(x) = \frac{1}{x}$.

2. Solution Steps

First, let's find $f(r(x))$. Since $r(x) = x+4$ and $f(x) = \frac{1}{x}$, we have:

$f(r(x)) = f(x+4) = \frac{1}{x+4}$

Next, we need to find $m(f(r(x)))$. Since $m(x) = 8x$ and $f(r(x)) = \frac{1}{x+4}$, we have:

$m(f(r(x))) = m(\frac{1}{x+4}) = 8(\frac{1}{x+4}) = \frac{8}{x+4}$

Now, let's analyze the transformations of $f(x) = \frac{1}{x}$ to obtain $m(f(r(x))) = \frac{8}{x+4}$.

* Reflection: There is no reflection across the x-axis or y-axis since there is no negative sign in front of the function or inside the function.

* Stretch/Compression: The function $\frac{1}{x}$ is multiplied by 8, which represents a vertical stretch by a factor of

8. * Vertical Shift: There is no vertical shift since there is no constant added or subtracted outside the fraction.

* Horizontal Shift: The term $x+4$ inside the function represents a horizontal shift. Since it's $x+4$, the graph shifts 4 units to the left.

3. Final Answer

1) $m(f(r(x))) = \frac{8}{x+4}$

2)

Reflection: None

Stretch/Compression: Vertical Stretch

Vertical Shift: None

Horizontal Shift: Left