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?

Short 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-by-step solution

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.