Question

How does the graph of g(x) = (x + 2)^3 − 7 compare to the parent function of f(x) = x^3

A) g(x) is shifted 2 units to the right and 7 units down.
B) g(x) is shifted 7 units to the right and 2 units up.
C) g(x) is shifted 2 units to the left and 7 units down.
B) g(x) is shifted 7 units to the left and 2 units down.

Answer 1

Answer: Option C

g(x) is shifted 2 units to the left and 7 units down.

Explanation:

If we have a main function
`f (x) = x ^ 3`

And we perform the transformation:

`g (x) = f (x + h) = (x + h) ^ 3`

Then it is fulfilled that:

If
`h> 0` the graph of f(x) moves horizontally h units to the left

If
`h <0` the graph of f(x) moves horizontally h units to the right

If we have a main function
`f (x) = x ^ 3`

And we perform the transformation:

`g (x) = f (x) + k = x ^ 3 + k`

Then it is fulfilled that:

If
`k> 0` the graph of f(x) moves vertically k units up

If
`k <0` the graph of f(x) shifts vertically k units down

In this case we have to:

`g(x) = (x + 2)^3 - 7`

Therefore
`h=2>0` and
`k = -7 <0`

This mean that: g(x) is shifted 2 units to the left and 7 units down

Answer 2

C

Explanation:

The tricky part is always what is in the brackets with the x. It is highly anti intuitive.

(x + 2) moves the graph left, not right as you might think. So from this, only C and D can be considered as answers.

Since the 2 is with the x, that's how many units left you will go -- 2 units.

C is the only possible answer.

The - 7 tells you it will move 7 units down. The 7 with a minus acts the way you think it should. It goes down which is what normally happens on a graph. A mnus number outside the brackets means down.