Graph the function y = √|x|.

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Accepted Answer

Hi everyone, let's take a look at this practice problem. This problem says graph the function Y is equal to the square root of the quantity of 36 multiplied by the absolute value of X in quantity using transformations on the graph of Y is equal to the square root of X. Below the problem we're given a graph that has our function Y is equal to the square root of X plotted on it. And below that we have another empty graph on which to plot our new function. So, we need to graph our function Y is equal to the square root of the quantity of 36 multiplied by the absolute value of X in quantity, using transformations on the graph of Y is equal to the square root of X. Now, if we look at our function, Y is equal to the square root of the quantity of 36 multiplied by the absolute value of X in quantity, the absolute value of X will extend the possible values of X, our domain that are applicable for this function. So the graph of Y is equal to the square root of X is only defined for non-negative values of X. But our other function, Y is equal to the square root of the quantity of 36 multiplied by the absolute value of X in quantity, is defined for all values of X. This also means that our function. is going to be symmetric about the Y axis, since we're going to have even symmetry. That's going to allow us to easily extend the graph using the Y equals to square root of X as our basis. We also noticed that if we rewrite our function, Y is equal to the square root of the quantity of 36, multiplied by the absolute value of X in quantity, that this is equal to 6 multiplied by the square root of the absolute value of X. So the transformation that we're looking for here is basically going to take the value of Y is equal to the square root of X and multiply it by 6 to get our new Y value. This means that a coordinate of X. Y on the graph of Y is equal to the square root of X is going to be transformed into the coordinate of, of X6Y on our new graph. So, we're gonna look at the graph of Y is equal to square root of X and look for some key points. And so, the first point we'll look at is the origin. So, we'll have 0.0. And that gets transformed to 0.0. So that point is the same in both graphs. Next point we'll look at is 1.1. And that gets transformed to 1.6. The next point that we'll look at is 4.2. And this gets transformed to 4.12. And the last point that we'll look at is the point of 9.3. And this gets transformed to 9.18. And so we're gonna use the fact that our function is gonna be symmetric about the y axis, as well as these transform points, to draw our new graph. So, we're gonna plot these points. So we'll have the point of 0.0, plotted on the graph. We'll then have the point of 1.6 plotted on this graph. But by symmetry, we're also going to have the point of -1.6. The next point we'll look at is 4.12. So we'll plot that point on the graph. And we'll also have the point of -4.12 as well. Due to the symmetry about the y axis. And then the final point that we're gonna look at is gonna be 9.18. And we'll also at the point of -9.18 as well, due to the um symmetry about the y axis. So now what we're going to do is actually connect these points with a smooth curve. And what we'll see is that The curve that we're going to be drawing here is going to be similar to the Y equal to square root of X, except we're now going to have By is extend into the negative range. And the slope of the graph is going to be much steeper due to the compression. By the comparison factor on the horizontal axis. So, the graph that we have drawn on the screen here is going to be the answer to this problem. So, I hope that this explanation has been useful, and I'll see you in the next video.

Graph the function y = √|x|.

Key Concepts

Absolute Value

Square Root Function

Graphing Functions

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