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Q. 66

Expert-verified
Found in: Page 103

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# 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?

The graph of the functions is given as

All three functions are even functions and pass through the same three points $\left(-1,1\right),\left(0,0\right),\left(1,1\right)$.

For $-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.

See the step by step solution

## 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 $\left(-1,1\right),\left(0,0\right),$and $\left(1,1\right)$.

For the region $-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.

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