Question

The function f(x) = -5x. The graph of g(x) is f(x) vertically compressed by a factor of 1/4 and reflected in the x axis. What is the function rule for g(x)?

g(x) = -20x
g(x) = -5/4x
g(x) = 20x
g(x) = -3x + 2

Answer 1

None of the above are correct, the correct answer is
g(x)=5/4x
because you multiply by 1/4 (the vertical, or towards the x axis compression) to get -5/4x
but then you have to reflect across the x axis by flipping the sign to get 5/4x
Try using a graphing tool to experiment with how changing numbers affects the line.

Answer 2

Answer:
`g(x)=(5)/(4)x`

Explanation:

We know that when we compress function h(x) by scale factor 'a', then the new compress function is represented as :-

`H(x)=a (\text{h(x)})`

Given : The function
`f(x) = -5x`

The graph of g(x) is f(x) vertically compressed by a factor of
`(1)/(4)`and reflected in the x axis.

Then , the function rule for F(x) after vertically compressed by a factor of
`(1)/(4)` will be :-

`F(x)=(1)/(4)f(x)=(1)/(4)(-5x)\\\\\Rightarrow\ F(x)=(-5)/(4)x`

After reflection across x-axis (sign gets change) the new function becomes :_

`g(x)=-F(x)=(5)/(4)x`