1. Graphing f(x) = ax^7
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Make a table to find points on the curve. Then plot and connect the points.
Graph:
Comparison to the graph of f(x)=x^2: There is a vertical stretch by a factor of 5 of the graph of f.
To graph the function we will make a table of values.
| x | 5x^2 | g(x)=5x^2 |
|---|---|---|
| - 1 | 5( - 1)^2 | 5 |
| - 0.5 | 5( - 0.5)^2 | 1.25 |
| 0 | 5( 0)^2 | 0 |
| 0.5 | 5( 0.5)^2 | 1.25 |
| 1 | 5( 1)^2 | 5 |
Let's now draw the parabola that connects the obtained points. We will also draw the parent function f(x)=x^2.
From the graph above, we can note the following.
From the graph and the observations above, we can conclude that the graph of g is a vertical stretch by a factor of 5 of the graph of f.