Question

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

Answer 1

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