In Exercises 55–59, use the graph of to graph each function g.

Question

Graph of f(x) showing a V-shaped function with vertex at (0,0) for college algebra transformations.

g(x) = f(x + 2) + 3

Accepted Answer

Welcome back. I am so glad you're here. We are given this function Y equals F of X. And that's given to us in this graphical representation here. And we are to graph the function G of X where G of X equals f of x minus two minus three. So what are the differences between our Y equals F of X and our G of X? Well We look here inside of the parentheses and we see that we have X -2 happening directly to our X. And then we also have this minus three happening outside of the parentheses. So what do each of those mean? Well, with this X -2 that's happening directly inside the parentheses happening to the X. So that indicates a horizontal shift. And because it is -2 we're subtracting two from the X. It means that we are going to move to the right two units from our origin. And how about this -3 happening at the end? Well because that's not happening directly to the X. That indicates a vertical shift. And for this one when vertical shifts happen, it is exactly what it says. So because it's a -3, it is going to go down three. So those are the two shifts taking place. We look at our Y equals F of X. That one has the origin at where we have the center of that function. And where's our new G of X functions? Center going to be Well for the X value that is going to go to the right to. So that will be too. And for the Y. value that's the vertical. That will be going down three. So that's -3. So we're going to be looking for something that is starting at to going to to the right on our X. Value and down three for our Y. Value. So that one will be more like this. Alright let's look for I'll write this down here. So we see it when we scroll down we're looking for a center at two -3. Let's look at our answer choices. Okay. Almost got it on screen. There we go. Okay where are all of our centers? Okay. For a. It is at two negative three. That one could work for B. It's at two positive three, nope. That one doesn't work for C. It's at negative two negative three. That one doesn't work and for D. It's at negative 23. That one doesn't work. The only one that works is our answer choice. A. Well done. We'll catch you on the next one.

In Exercises 55–59, use the graph of to graph each function g.
g(x) = f(x + 2) + 3

Key Concepts

Function Transformation

Vertex of a Function

Graphing Techniques

Watch next