Math Snap

STEP 1

Assumptions1. The parent function is $f(x)=x^{}$.
. The function is shifted1 unit to the right.
3. The function is vertically stretched by a factor of5.
4. The function is reflected over the $x$-axis.

STEP 2

First, let's understand what each transformation does to the function.- A shift1 unit to the right changes $f(x)$ to $f(x-1)$.
- A vertical stretch by a factor of5 changes $f(x)$ to $5f(x)$.
- A reflection over the $x$-axis changes $f(x)$ to $-f(x)$.

STEP 3

Now, let's apply these transformations one by one to the parent function $f(x)=x^{2}$.First, apply the shift1 unit to the right. This changes $f(x)=x^{2}$ to $f(x-1)=(x-1)^{2}$.

STEP 4

Next, apply the vertical stretch by a factor of. This changes $f(x-1)=(x-1)^{2}$ to $f(x-1)=(x-1)^{2}$.

STEP 5

Finally, apply the reflection over the $x$-axis. This changes $5f(x-1)=5(x-1)^{2}$ to $-5f(x-1)=-5(x-1)^{2}$.

So, the equation of the new function after applying all the transformations is $g(x)=-5(x-1)^{2}$.
Looking at the options, the correct answer is option B $g(x)=-5(x-1)^{2}$.