Question

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

Answer 1

Answer: Option C

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

Step-by-step 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 $h$ 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 $k$ 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 $k = -7$

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

Answer 2

Answer:

C

Step-by-step 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.