### Home > A2C > Chapter 4 > Lesson 4.2.1 > Problem4-85

4-85.

Given $f(x)=x^3+1$  and  $g(x)=(x+1)^2$:

1. Sketch the graphs of the two functions.

What are the parent graphs of each function? How is each function transformed?

1. Solve $f(x)=9$.

Solve: $9=x^3+1$

1. Solve $g(x)=0$.

See part (b).

1. Solve $f(x)=−12$.

See part (b).

1. Solve $g(x)=−12$.

See part (b).

1. For how many values of $x$ does $f(x)$ equal $g(x)$?  Explain.

Look at the graph from part (a).

Three values because the graphs cross three times.

2. Find and simplify an expression for $f(x)−g(x)$.

$x^3−x^2−2x$

Use the eTool below to solve the parts of the problem.
Click the link at right for the full version of the eTool: CCA2 2-101 HW eTool