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It is asking me to graph a function with transformations y=3f(x) but the function they gave me to start out with looks like an absolute value?It is #35

It is asking me to graph a function with transformations y=3f(x) but the function-example-1
User Ktheory
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1 Answer

21 votes
21 votes

From the graph of f(x)

The parent function of the absolute value is


y=\lvert x\rvert

And its graph is

Since the graph of f(x) has its vertex at (0, 3)

Then f(x) is the image of the parent function after reflection on the x-axis and translated 3 units up

Then change the sign of y and add it by 3

Then the function f(x) is


f(x)=-\lvert x\rvert+3

And its graph is the blue one in the figure

Now we will stretch it by a scale factor of 3


y=3f(x)

Let us draw the graph

It is the green graph

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User Jamie Burns
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