Using transformations, determine the coordinates of the key point (0, 1) on the graph of the function...

Question

^f(x)=-e^x+4.

 

A. (0,1)

B. (0,5)

C. (-4,-1)

D. (-4,1)

E. None of the above

Answer 1

I am assuming that the point (0,1) is on the graph of y = e^x.

 

To get the graph of f(x) = -e^x+4, you will:

 

1) Shift the graph of e^x 4 units to the left, then

2) Reflect across the x-axis.

 

Staring with (0,1), the first transformation moves it to (-4,1), and then the second moves this point to (-4,-1).

 

You can check this answer by plugging x = -4 into f(x): f(-4) = -e^-4+4 = -e⁰ = -1. This confirms that (-4,-1) is the correct answer. Choose C.