Question

If you apply these changes to the linear parent function, f(x)=x, what is the equation of the new function? Vertically compress by a factor of 4. Reflect over the x-axis . A. G(x) = 4 - x B. G(x) = - 1/4 * x C. G(x) = 1/4 * x D. G(x) = - 4x

Answer 1

Answer:g(x)=-1/4x

Step-by-step explanation:

Answer 2

Given:

The linear parent function, f(x)=x is vertically compressed by a factor of 4 and reflected over the x-axis.

To find:

The new function.

Solution:

The vertical stretch and compression is defined as

$g(x)=kf(x)$

If k>1, then f(x) vertically stretched by factor k and if 0<k<1, then f(x) vertically compresses by factor $\dfrac{1}{k}$.

In the given problem, linear parent function, f(x)=x is vertically compressed by a factor of 4. So, $k=\dfrac{1}{4}.$

$g(x)=\dfrac{1}{4}f(x)$

Then, it is reflected over the x-axis.

$G(x)=-g(x)$

$G(x)=-\dfrac{1}{4}f(x)$       $[\because g(x)=\dfrac{1}{4}f(x)]$

$G(x)=-\dfrac{1}{4}x$       $[\because f(x)=x]$

So, the new function is $G(x)=-\dfrac{1}{4}x$.

Therefore, the correct option is B.