How does the graph of g(x) = (x − 1)3 + 5 compare to the parent function f(x) = x3?

g(x) is shifted 1 unit to the right and 5 units up.
g(x) is shifted 5 units to the right and 1 unit up.
g(x) is shifted 1 unit to the left and 5 units up.
g(x) is shifted 5 units to the right and 1 unit down.

A

Step-by-step explanation:

Given:

- The original function is:

                               f(x) = x^3

Find:

How does the graph of g(x) = (x − 1)3 + 5 compare to the original function.

Solution:

- We have a general form of the new function relating to parent function.

                               g(x) = a*( x +/- b )^n + c

Where; a, b and c are constants.

- The constant a magnitude denotes steepness of the graph relative to 1 and the sign of a will determine the mirror image of the graph about line y = 0.

- The constant b magnitude denotes shifts of the graph of every x value sign of b will determine the direction of shifts. + b : shift left , - b shift right.

- The constant c magnitude denotes shifts of the graph of every y value. sign of c will determine the direction of shifts. + c : shift up , - b shift down.

- In our g(x).   a = 1 , b = -1 , c = + 5

Hence, g(x) is shifted 1 unit to the right and 5 units up.

step-by-step explanation: