Point Plotting

Question

I'm having trouble with the below question. I don't exactly understand how to answer the question.

 

Suppose (3,-4) is on the graph of y=f(x). Use Theorem 1.7 to find a point on the graph of the following transformed function.

 

y=2f(x-7)+3

Answer 1

Well, you didn't tell us what "Theorem 1.7" is, but here's how the function transform moves the point (3,-4):

 

• The f(x-7) part shifts the x-coordinate 7 units to the right (positive direction):

 

         (3,-4) → (3+7,-4) = (10,-4)

 

• The factor of 2, 2f(x-7), then stretches the y-coordinate vertically by a factor of 2:

 

         (10,-4) → (10,-4*2) = (10,-8)

 

• Finally, the +3, 2f(x-7)+3, lifts the y-coordinate up three units:

 

         (10,-8) → (10,-8+3) = (10,-5)

 

So the function transform moves (3,-4) to (10, -5)