Question

Question 3(Multiple Choice Worth 5 points)

(03.03 LC)

How does the graph of g(x) = (x − 2)3 + 7 compare to the parent function f(x) = x3?

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

Answer 1

Answer: Second option.

Explanation:

Below are some transformation for a function f(x):

If
`f(x)+k` then the function is shifted up "k" units.

If
`f(x)-k` then the function is shifted down "k" units.

If
`f(x+k)` then the function is shifted "k" units to the left.

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

Knowing this tranformations and given the parent function
`f(x)=x^3` and the function
`g(x) = (x -2)^3 + 7`, we can conclude that the function g(x) is shifted 2 units to the right and 7 units up.

We can observe that this matches with the second option.