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QuestionFind the new function from f(x)=xf(x)=x after a vertical stretch by 3 and a flip over the xx-axis. A. g(x)=3x−1g(x)=3 x-1 B. g(x)=3xg(x)=\frac{3}{x} C. g(x)=−13xg(x)=-\frac{1}{3} x D. g(x)=−3xg(x)=-3 x

Studdy Solution

STEP 1

Assumptions1. The parent function is f(x)=xf(x)=x . The function is to be vertically stretched by a factor of33. The function is to be flipped over the xx-axis

STEP 2

First, let's understand what a vertical stretch by a factor of means. It means that the y-values of the function are multiplied by.g(x)=f(x)g(x) =f(x)

STEP 3

Now, plug in the given parent function f(x)=xf(x)=x into the equation.
g(x)=3xg(x) =3x

STEP 4

Next, let's understand what flipping over the x-axis means. It means that the y-values of the function are multiplied by -1.g(x)=−g(x)g(x) = -g(x)

STEP 5

Now, plug in the function g(x)=3xg(x) =3x into the equation.
g(x)=−3xg(x) = -3xSo, the new function after applying the changes is g(x)=−3xg(x) = -3x.
Looking at the options, the correct answer is D. g(x)=−3xg(x)=-3 x.

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