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Describe the parent function, then use a table of values to graph the functions.
Graph:
Transformation:A vertical shrink by a factor of 12.
The given function is an absolute value function, so its parent function is y=|x|. We will start by graphing both functions in one coordinate plan. Then we will compare them to describe the transformation.
To graph both of the functions, we will use a table of values. We will choose a variety of x-values: at least one negative, 0, and at least one positive.
x | y=|x| | f(x)=1/2|x| |
---|---|---|
-4 | |-4|= 4 | 1/2|-4|= 2 |
0 | |0|= 0 | 1/2|0|= 0 |
4 | |4|= 4 | 1/2|4|= 2 |
Now let's plot the functions using these points! Remember that the graph of absolute value functions is V-shaped.
Having drawn our functions, we can describe the transformation.
We see that each y-value is being multiplied by 12 and all points are being pushed towards the x-axis. This is a vertical shrink by a factor of 12.