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

4-85.

Given

*f*(*x*) =*x*^{3}+ 1 and*g*(*x*) = (*x*+ 1)^{2}: 4-85 HW eTool (Desmos). Homework Help ✎Sketch the graphs of the two functions.

Solve

*f*(*x*) = 9.Solve

*g*(*x*) = 0.Solve

*f*(*x*) = −12.Solve

*g*(*x*) = −12.For how many values of

*x*does*f*(*x*) equal*g*(*x*)? Explain.Find and simplify an expression for

*f*(*x*) −*g*(*x*).

Use the eTool below to solve the parts of the problem.

Click the link at right for the full version of the eTool: A2C 4-85 HW eTool

You can sketch a graph of *g*(*x*) and use a table to graph *f*(*x*).

Substitute 9 for *f*(*x*) and solve.

See part (b).

See part (b).

See part (c).

Look at the graph from part (a).

Three because the graphs cross three times.

*x*^{3} − *x*^{2} − 2*x*