Question

The parent function f(x)=x^3 is transformed to g(x)=x^3+2 and to h(x)=(x+2)^3. both transformations involve the same constant, but the placement of the constant differs. using your knowledge of transformations, describe how you think the graph of the parent function will change with each transformation. then sketch the graphs of the parent function and the two transformations and compare your results with your description.

Answer 1

Answer:

See explanation.

Step-by-step explanation:

$f(x)=x^3\\g(x)=x^3+2$

The added 2 to the end of the equation suggests a shift 2 units upward.

SEE IMAGE #1

$f(x)=x^3\\h(x)=(x+2)^3$

A 2 added directly to the x variable which is cubed alongside the x suggests a shift 2 units to the left.

SEE IMAGE #2

The first image shows your first translated function, the second image shows your second translated function. Your parent function [f(x)] is in red, your child functions are in blue.

Transformations within the parantheses are opposite than you may think:

Adding a number within parantheses suggests a shift to the left (more negative), while subtracting a number within parantheses suggests a shift to the right (more positive).