Question

Write the function with the given transformation from the given parent function. f(x) = 3square root x reflected across the x-axis vertically stretched by a factor of 7 shifted left 4

Answer 1

Answer:

$f(x)=-21\sqrt{x+4}$.

Step-by-step explanation:

We have been given a parent function $f(x)=3\sqrt{x}$.  We are asked to reflect our given function across the x-axis, vertically stretch by a factor of 7, shifted left 4.

We will perform the transformation in the given order.

First of all, we will reflect the function  $f(x)=3\sqrt{x}$. across x-axis.

We know that when a function g(x) is reflected x-axis it becomes $-g(x)$, so our function after reflection across x-axis would be $f(x)=-3\sqrt{x}$.

Now, we will vertically stretch the function.

We know that to stretch a function g(x) vertically, we need to multiply it by factor of stretch. So our function after vertical stretched by a factor of 7 would be $f(x)=7(-3\sqrt{x})=-21\sqrt{x}$.

To shift graph by 4 units to left, we will add 4 under square root function as:

$f(x)=-21\sqrt{x+4}$

Therefore, our required function would be $f(x)=-21\sqrt{x+4}$.