Q. 66 - Precalculus Enhanced with Graphing Utilities

Question

Exploration Graph $y=x^2,y=x^4$, and $y=x^6$ 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 functions are even functions and pass through the same three points $(-1,1),(0,0),(1,1)$.

For $-1<x<1$, the graph of $y=x^2$ lies above the other two graphs.

And for the region $x<-1,x>1$, the graph of $y=x^6$ lies above the other two.

Step 1. Graph the functions

The graph of the functions $y=x^2,y=x^4$, and $y=x^6$ on the same coordinate plane is given as

Step 2. Comparision

From the graph, it can be seen that all three graphs have the same general shape.

All three functions are even.

All three functions pass through the points $(-1,1),(0,0),$and $(1,1)$.

For the region $-1<x<1$, the graph of $y=x^2$ is above the other two.

And for the region $x<-1,x>1$, the graph of $y=x^6$ lies above the other two.