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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.

User Pepijn
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7.9k points

2 Answers

1 vote

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

User Rossen Stoyanchev
by
8.1k points
3 votes

Answer:

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.

User Don Mackenzie
by
7.8k points

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