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Describe the parent function and then use slope to graph the functions.
Graph:
Transformation: A vertical stretch by a factor of 3.
The given function is linear, so its parent function is y=x. We will start by graphing both functions in one coordinate plane. Then we will compare them to describe the transformation.
To graph both of the functions, we will use their slopes and y-intercepts.
| Function | Slope-intercept form | Slope | y-intercept |
|---|---|---|---|
| y=x | y= 1x+ 0 | 1 | 0 |
| y=3x | y= 3x+ 0 | 3 | 0 |
Having drawn our functions, we can describe the transformation.
We see that each y-value is being multiplied by 3 and all points are being pulled away from the x-axis. This is a vertical stretch by a factor of 3.