What transformation produce the graph of g(x)=5^(-x+2) from the graph of the parent function f(x)=5^x? Select all that apply.

Question

What transformation produce the graph of g(x)=5^(-x+2) from the graph of the parent function f(x)=5^x? Select all that apply.

a. reflection over the x-axis

b. reflection over the y-axis

c. horizontal shift to the left 2 units

d. horizontal shift to the right 2 units

e. vertical shift up 2 units

f. vertical shift down 2 units.

Answer 1

You need to factor out (-1) in the exponent first.

g(x)=5^(-x+2) = g(x)=5^[-(x-2)]

The answer will have two steps. The graph of 5^[(x-2)] requires a shift to the right by 2 units.

Then from here the graph of g(x) = 5^[-(x-2)] requires a reflection on the y axis.

The final answer therefore will be d) AND b).

Answer 2

The correct answer here is c

Shift to the left two units