Q. 67 - Precalculus Enhanced with Graphing Utilities

Question

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

Step-by-Step Solution

Answer

The graph of the functions is given as

All three graphs have the same general shape and go through the points $(-1,-1),(0,0),$ and $(1,1)$. As the exponent increases, the steepness of the curve increases. 

Step 1. Graph the functions

The graph of the functions $y=x^3,y=x^5,$ and $y=x^7$ on the same coordinate plane is given as

Step 2. Comparision

The three graphs have the same general shape.

Also, the three graphs go through the points $(-1,-1),(0,0),(1,1)$.

The three functions are odd and as the exponent increases, the steepness of the curve increases.