How do you obtain the graph of

Question

How do you obtain the graph of $y=f\left(x+2\right)$ from the graph of $y=f\left(x\right)$ ?

Accepted Answer

Hello there today we're gonna solve the following calculus problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. Given the function Y equals G of X. How would the graph of Y equals G of X minus three differ from the original graph? Awesome. So it appears for this particular pro we're comparing two different functions. So we're comparing Y equals G of X to Y equals G of X minus three. And we're asked to determine how would the graph for Y equals G of X minus three differ from G of X or Y equals G of X to be exact. So now that we know what we're solving for, let's read off our multiple choice answers to see what our final answer might be. A is the graph shifts three units downwards B is the graph shifts three units upwards. C is the graph shifts three units to the left and D is the graph shifts three units to the right? Awesome. So first off, let us break down solving this particular problem into four. Easy to follow steps. So let's write that down. So 123 and four, so we can solve this particular problem in four simple steps. So first off, we need to note that we are given the function Y equals G of X. So let's write that here. So Y equals G FX. And we're also trying to figure out how would the graph Y equals G of X minus three differ from Y equals G of X. So our first step is we need to identify the given function as Y equals G of X. And we're asked to compare this with the graph of Y equals G of X minus three. So we've identified. So let's make it put a letter capital I to note that we're identifying what exactly we're solving for. Our second step is we need to understand. So we're gonna denote this as you, we need to understand that the transformation of Y equals G of X minus three involves a horizontal shift of the graph of Y equals G of X. So I'm gonna denote this as HS which is horizontal shift. So three, our second, sorry. So our second step was to understand that the transformation of Y equals G of X minus three will involve a horizontal shift. So considering that moving on to our third step, we need to recognize which I'm gonna denote as R, we need to recognize that the subtraction inside the function argument. So let's underline that in red. So the subtraction which is X minus three. So the subtraction inside of this function argument, this X minus three will indicate a shift to the right by three units. So shift to right by three units. So it's gonna be going three units to the right. So I have an arrow pointing to the right. So because it's X minus three, that means that it will be indicating a shift to the right by three units. Whereas if this was X plus three, then that means it'd be moving three units to the left. So if it's plus, it's going to the left, if it's minus, it's going to the right. Awesome. So now moving on to our fourth and final step, which we need to make our final conclusions. So our final conclusions, we need to conclude that the graph of Y equals G of X minus three will be the same as Y equals G of X, but it will be shifted three units to the right along the X axis. So, meaning, so we need to note that it will be the same, but it's gonna be shifted to the right. So shifted to right by three units along the X axis. Awesome. And that's it. So that will mean without a doubt, looking at our multiple choice answers, our final answer has to be the letter D, the graph will shift or shifts three units to the right and that's it. Thank you. So much for watching. Hopefully that helped. And if you any, if anything didn't make sense, I would suggest going back to look in your chapter, read over on how to solve this type of problem. So it's very important to understand the background context. So you need to know the difference between X minus three and X plus three, that's very important. So as long as you have the basics for like like certain things to note, so you'll know what to solve for when you, you'll know what to solve. For. As long as you understand that X minus three means that you're gonna be shifting to the right. Whereas X plus three, you're gonna be shifting to the left if you understand little tidbits of information like that solving a problem like this is very easy to do and that's it. Thank you so much for watching once again. I hope that helped and I hope to see you in the next video. Bye.

How do you obtain the graph of $y=f\left(x+2\right)$ from the graph of $y=f\left(x\right)$ ?

Key Concepts

Function Transformation

Horizontal Shifts

Graphing Functions

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