Question

the graph of f(x) can be compressed vertically and shifted to the left to produce the graph of g(x). if f(x) =x^3, which of the following could be the equation of g(x)?

Answer 1

Answer:
`B.\ g(x)=(1)/(4)(x+3)^3`

Explanation:

The misssing options are:

`A.\ g(x)=4(x-3)^3\\\\B.\ g(x)=(1)/(4)(x+3)^3\\\\C.\ g(x)=4(x+3)^3\\\\D.\ g(x)=(1)/(4)(x-3)^3`

Some transformations for a function f(x) are shown below:

1. If
`f(x-k)`, the function is shifted right "k" units.

2. If
`f(+k)`, the function is shifted left "k" units.

3. If
`bf(x)` and
`b>1`, the function is stretched vertically by a factor of "b".

4. If
`bf(x)` and
`0<b<1`, the function is compressed vertically by a factor of "b".

In this case, you know that the parent function f(x) is:

`f(x)=x^3`

If the graph of the function g(x) is obtained by compressing vertically and shifting the function f(x) to the left, then:

`g(x)=bf(x+k)` and
`0<b<1`

Based on this, you can identify that the following function could be the equation of the g(x):

`g(x)=(1)/(4)(x+3)^3`