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

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
`(1)/(k)`.

In the given problem, linear parent function, f(x)=x is vertically compressed by a factor of 4. So,
`k=(1)/(4).`

`g(x)=(1)/(4)f(x)`

Then, it is reflected over the x-axis.

`G(x)=-g(x)`

`G(x)=-(1)/(4)f(x)`
`[\because g(x)=(1)/(4)f(x)]`

`G(x)=-(1)/(4)x`
`[\because f(x)=x]`

So, the new function is
`G(x)=-(1)/(4)x`.

Therefore, the correct option is B.