Chapter 4.1, Problem 130E

To determine

To sketch: The graphs and describe the transformation.

Answer to Problem 130E

From the graphs it is clear that, the function $f\left(x\right)=x^3$ and move three spaces left: $g\left(x\right)=-{\left(x+3\right)}^3$

Explanation of Solution

Given information: $f\left(x\right)=x^3,g\left(x\right)=-{\left(x+3\right)}^3$

Calculation: Use graphing device to graph the function $f\left(x\right)=x^3$.

Graph : Sketch the graph using graphing utility.

Step 1: Press WINDOW button to access the Window editor.

Step 2: Press $\boxed{\text{Y=}}$ button.

Step 3: Enter the expression $x^3$ which is required to graph.

Step 4: Press GRAPH button to graph the function and adjust the windows according to the graph.

The graph is obtained as:

  

Use graphing device to graph the function $g\left(x\right)=-{\left(x+3\right)}^3$.

Graph : Sketch the graph using graphing utility.

Step 1: Press WINDOW button to access the Window editor.

Step 2: Press $\boxed{\text{Y=}}$ button.

Step 3: Enter the expression $-{\left(x+3\right)}^3$ which is required to graph.

Step 4: Press GRAPH button to graph the function and adjust the windows according to the graph.

The graph is obtained as:

  

Description of the transformation,

From the graphs it is clear that, the function $f\left(x\right)=x^3$ and move three spaces left: $g\left(x\right)=-{\left(x+3\right)}^3$