Question

How does the graph of g(x) = (x − 8)3 + 3 compare to the parent function f(x) = x3?

Answer 1

Answer:

C. g(x) is shifted 8 units to the right and 3 units up.

Step-by-step explanation:

We have been given two functions formula. We are asked to compare the the graph of function $g(x)=(x-8)^3+3$ to graph of parent function $f(x)=x^3$.

Let us recall translation rules.

$f(x)\rightarrow f(x-a)=\text{Graph shifted to right by a units}$

$f(x)\rightarrow f(x+a)=\text{Graph shifted to left by a units}$

$f(x)\rightarrow f(x)-a=\text{Graph shifted downwards by a units}$

$f(x)\rightarrow f(x)+a=\text{Graph shifted upwards by a units}$

Upon looking at translation rules, we can see that graph of $f(x)$ is shifted to right by 8 units and 3 units upwards to get the graph of $g(x)$.

Therefore, option C is the correct choice.

Answer 2

Answer:

C.

Step-by-step explanation:

because it is x-8, it will shift to the right because it is always the opposite of the symbol. +3 refers to the points going up