Question

Please help me out!!!

Answer 1

Shifts 4 units down --->
`g(x)=2x-10`

Stretches f(x) by a factor of 4 away from x-axis--->
`g(x)=8x-6`

Shifts f(x) 4 units right--->
`g(x)=2x-14`

Compress f(x) by a factor of 1/4 toward the y-axis --->
`g(x)=1/2x-3/2`

Explanation:

We are given
`f(x)=2x-6`

We need to match the transformations.

1) shifts f(x) 4 units down.

When function f(x) shifts k units down the new function becomes f(x)-k

In our case

`g(x)=2x-6-4\\g(x)=2x-10`

So, Shifts 4 units down --->
`g(x)=2x-10`

2) Stretches f(x) by a factor of 4 away from x-axis

When function f(x) is stretched by a factor of b away from x-axis the new function becomes f(bx)

`g(x)=2(4x)-6\\g(x)=8x-6`

So, Stretches f(x) by a factor of 4 away from x-axis--->
`g(x)=8x-6`

3) Shifts f(x) 4 units right

When function f(x) shifts h units right the new function becomes f(x-h)

`g(x)=2(x-4)-6\\g(x)=2x-8-6\\g(x)=2x-14`

So, Shifts f(x) 4 units right--->
`g(x)=2x-14`

4) Compress f(x) by a factor of 1/4 toward the y-axis

When function f(x) is compressed by h factor of a toward the y-axis the new function becomes h.f(x)

`g(x)=1/4(2x-6)\\g(x)=1/2x-3/2`

Compress f(x) by a factor of 1/4 toward the y-axis --->
`g(x)=1/2x-3/2`

(Option Not given)

(If we compress f(x) by a factor of 4 towards y-axis we get g(x)=8x-24)