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.

-x indicates a reflection over the y-axis

-x+2 = -(x-2) so a shift to the right
the question is, which was done first?
Graph the curves to verify

b and d

Thank you oobleck!

Well, well, well, we've got ourselves a transformation question! Time to put on my clown shoes and bring out the humor!

Let's analyze each option and see which ones apply here, shall we?

a. Reflection over the x-axis: Imagine the graph of the parent function lying on a trampoline. If you jump on it hard enough, it might just flip upside down! So, does g(x) do a somersault over the x-axis? No, it doesn't. So, cross this option out like flipping a pancake.

b. Reflection over the y-axis: Picture the graph of the parent function standing in front of a mirror. If it flashes a smile, will g(x) give us a mirrored frown? Nope! So, toss this option away like throwing an unwanted souvenir.

c. Horizontal shift to the left 2 units: If f(x) is like a party animal that shifts, dances, and hops around the x-axis, does g(x) join in on the fun but move 2 units to the left? Yes, it does! So, grab your dancing shoes and keep this option firmly on the table!

d. Horizontal shift to the right 2 units: Now, if f(x) is busy shaking its groove thing to the right, will g(x) follow suit and shift an extra 2 units in the same direction? Nope, it's not in the mood to go right, so kick this option out like a tired kangaroo.

e. Vertical shift up 2 units: Imagine f(x) as a basketball player trying to dunk the ball into the hoop. Will g(x) channel its inner Michael Jordan and rise up 2 units? No jams here! So, bounce this option away like a deflated basketball.

f. Vertical shift down 2 units: If f(x) is reaching the high notes and flying in the sky, does g(x) plummet down 2 units to the ground with a thud? Bingo! This option stays, so you've got a winner, winner, chicken dinner!

So, in conclusion, the correct transformations for the graph of g(x)=5^(-x+2) are:

c. Horizontal shift to the left 2 units
f. Vertical shift down 2 units

Hope this made you smile like a clown with a rubber chicken!

To determine the transformations that produce the graph of g(x) = 5^(-x+2) from the graph of f(x) = 5^x, we need to compare the two functions and analyze the changes made to the parent function.

First, let's look at the term inside the exponent: -x + 2. This tells us that the function has a horizontal shift to the right by 2 units, as the "-x" part represents a reflection over the y-axis. Therefore, the correct answer is:

d. horizontal shift to the right 2 units.

Next, let's focus on the term outside the exponent: 5^( -x+2). Here, we have a vertical shift up by 2 units, as the "+2" part shifts the graph upward. Therefore, the correct answer is:

e. vertical shift up 2 units.

In summary, the transformations that produce the graph of g(x) = 5^(-x+2) from the graph of f(x) = 5^x are a horizontal shift to the right 2 units and a vertical shift up 2 units. So, the correct answers are d and e.