Question

How does the graph of g(x) = (x - 3)^3 - 2 differ from the group of f(x) = x^3?

A. g is shifted 3 units right and 2 units up.
B. g is shifted 3 units right and 2 units down.
C. g is reflected across the y-axis.
D. g is rotated 90* clockwise.

Answer 1

B

Explanation:

f(x) = x³

g(x) = (x - 3)³ - 2

The inside of the parenthesis represents a horizontal shift

If the number operation being done to x inside of the parenthesis is adding ( or if the number is positive ) then the graph will shift to the left. If the operation being done inside of the parenthesis to x is subtraction ( or if the number is negative ) then the graph will shift to the right.

The operation being done is subtraction therefore it will shift to the right. So it will go 3 units to the right.

the number on the outside works like a y intercept. if it's positive it goes up, if it's negative it goes down. the number is -2 so it will go down 2 units

we can conclude that g is shifted 3 units right and 2 units down

the answer is B