1. Graphing f(x) = ax^10
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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 3 followed by a reflection in the x-axis of the graph of f.
To graph the function we will make a table of values.
| x | - 3x^2 | p(x)=- 3x^2 |
|---|---|---|
| - 2 | - 3( - 2)^2 | - 12 |
| - 1 | - 3( - 1)^2 | - 3 |
| 0 | - 3( 0)^2 | 0 |
| 1 | - 3( 1)^2 | - 3 |
| 2 | - 3( 2)^2 | - 12 |
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 p is a vertical stretch by a factor of 3 followed by a reflection in the x-axis of the graph of f.