Shifting Graphs

Exercises 27...

Question

Shifting Graphs

Exercises 27–36 tell how many units and in what directions the graphs of the given equations are to be shifted. Give an equation for the shifted graph. Then sketch the original and shifted graphs together, labeling each graph with its equation.

y = −√x Right 3

Accepted Answer

Below there. Today we're going to solve the following practice 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. Write the new equation after shifting the given graph as stated below. Also plot bold graphs using the same rectangular coordinate system. Y equals the square root of 5 X left 8 units. Awesome. So it appears for this particular problem, we're asked to solve for two separate answers. Our first answer that we're trying to ultimately solve for is we're trying to write our new equation after shifting our given graph, which in this case, it's a given equation, means we're trying to create the graph. So we're trying to take our equation, which is Y equals the square root of 5 X, and we're trying to rewrite that equation after the shift takes place because we're told to move our given equation left 8 units. So that's our first answer we're trying to figure out what our new equation will be once we've shifted our original equation function. Left 8 units, that's our first answer. And then our second answer is we're trying to graph both our original function, which is Y equals the square root of 5 X. And we're also trying to graph our new equation once it's been shifted 8 units to the left. Awesome. So now that we know that we're ultimately trying to solve for two separate answers, what we need to do first off is and we need to recall and note that in order to shift our graph of Y equals the square root of 5 X. 8 units to the left, we will need to modify our equation as follows. So since we're shifting our graph 8 units to the left, so in order to do that, we need to shift our graph to the left by H amount of units. So we need to replace X with drum roll. Parentheses X plus H. So for a shift of 8 units to the left to occur, the new equation would have to be Y equals the square root of 5 multiplied by X + 8, and that is our new equation. Hooray, we did it. We solve for one of our final answers. Hooray, we did it. So now, moving right along now, to quickly summarize what we've learned so far. we need to note that the graph of Y equals the square root of 5 X is shifted 8 units to the left, and the new equation, once the shift has occurred, will be Y equals the square root of 5 multiplied by X + 8. So now, let us, let's figure out some points to help us plot our original function for Y equals the square root of 5 X. So right now we're going to shift our focus on trying to graph Y equals the square root of 5 X. So trying to figure out some points to plot, so let us know that at X equals 0, that will mean that Y equals 0, and when X is equal to 5, that will mean that Y. is going to be equal to 5. So that will mean, so when X is equal to 0 and Y is equal to 0, that means our coordinate point will be 0.0 in parentheses. And when X is equal to 5, Y will be equal to 5, so our coordinate point will be 5.5. And when X is equal to 20, that will mean that Y will be equal to 10, so that will mean our coordinate point will be at 2010 in parentheses. And finally, one more coordinate point. When X is equal to 45, that will mean that Y is going to be equal to 15, which will mean that our coordinate point will be 45.15. In parentheses. And once again, this is when we plug in different values of X into our equation. So it'll be like 5 multiplied by 05 multiplied by 55 multiplied by 20, etc. So, with that said, those are 5 different those are 4 different coordinate points. We don't need 5, you could do 5 if you wanted to, but it's usually when you're graphing a curve, it's good to have at least minimum 3 different points to plot on your graph. So having a nice 4 different points to graph is really nice. This will help make your overall curve more accurate when you're plotting it on your graph. So, with that said, moving right along now, let us plot some points for our shifted graph. So now we're gonna focus our attention for when Y is equal to the square root of 5 multiplied by X + 8. Fantastic. So now we're gonna be trying to graph our shifted graph. So let's do 4 different coordinate points once again. So, when X is equal to -8, that will mean that Y is going to be equal to 0. So that means our coordinate point will be -8.0. When X is equal to -3, that will mean that Y is going to be equal to 5, so our coordinate point will be -3.5. And then finally, For our third corner point, when X is equal to 12, that will mean that Y is going to be equal to 10, so our coordinate point will be 12.10 in parentheses. And finally, when X is equal to 37, that will mean that Y is going to be equal to 15, so that will mean that our coordinate point will be 37.15 in parentheses. And just for fun, let's add one more coordinate point. So when X is equal to 72, Y will be equal to 20, so that will mean that our coordinate point will be 72.com. 20 So now all we need to do is we need to plot both of our curves and let us say that We'll have our shifted curve. To be in green, and we'll make our original curve to be in red. Awesome. So, essentially, when we plug in our two different functions into our graphing software of choice, we should be able to produce the following graph. And as you could see, Our shifted graph has just been shifted to the left 8 units, and it's represented in green, and as you can see, we have our different coordinate points labeled on our graph, and as you can see, it's the same exact shape of the curve for our original curve, which is represented in red. However, it's just been shifted to the left 8 units. And that's it. Those are our final two answers. We've officially graphed our two curves, and we've come up with the equation for our shifted crap for our shifted equation. And that's it. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Shifting Graphs

Exercises 27–36 tell how many units and in what directions the graphs of the given equations are to be shifted. Give an equation for the shifted graph. Then sketch the original and shifted graphs together, labeling each graph with its equation.

y = −√x Right 3

Key Concepts

Graph Shifting

Square Root Function

Equation Transformation

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