Chapter 2.4, Problem 67AYU

In Problems 64-71, use a graphing utility.

Exploration Graph $y=x^3,y=x^5,\text{ and }y=x^7$ on the same screen. What do you notice is the same about each graph? What do you notice is different?

To determine

To graph: Graph the equations $y = x^3, y = x^5$ and $y = x^7$. Then conclude common things about each graph.

Answer to Problem 67AYU

Explanation of Solution

To sketch:

Graph the following equation with the graphing utility:

1. $y = x^3$

2. $y = x^5$

3. $y = x^7$

Interpretation:

The equation $y = x^3$ is a cube curve and passes through the vertex point $\left(0,0\right)$.

All three curves pass through the same point $\left(0,0\right)$ As the exponent increases, the corresponding steepness also increases.