![]() You've essentially flipped it over the y. Square root of negative x is going to look like this. Saw at x equals four, you will now see at xĮquals negative four, and so on and so forth. You saw at x equals two, you would now see at Now this one won't beĭefined for positive numbers. So the square root of x is notĭefined for negative numbers. What would that do to it? Well, whatever was happeningĪt a certain value of x will now happen at the So let's say we want to now figure out what is the graph of y isĮqual to the square root of? Instead of an x under the radical sign, let me put a negative x Y equals the square root of x looks like, but let's say we just want to build up. And the way that I'm going to do that is I'm going to do it step by step, so we already see what Times the square root of negative x minus one should look like, and then I'll just lookĪt which of the choices is closest to what I drew. ![]() Through this together, and the way that I'm going to do it is I'm actually going to try to draw what the graph of two Which of the following is the graph of y is equal to two times the square root of negative x minus one? And they give us some choices here, and so I encourage you to pause this video and try to figure it out on your own before we work through this together. The graph of y is equal to square root of x is This skill is especially important in Calculus, when we pay more attention to the maxima and minima of the function. Graphing functions by hand is usually not a super precise task, but it helps you understand the important features of the graph. (3.) Thus to draw the function, if we have the general picture of the graph in our head, all we need to know is the x-y coordinates of a couple squares (such as (2, 4)) and then we can graph the function, connecting the dots. (2.) This square root function will only be defined for x>=0, unless we are dealing with imaginary numbers (negative numbers under the square roots). To prove this, take any infinitely larger y-value, and I can get you an x-value that is equal to that valued squared. Although the graph does not increase very fast, as x gets larger y will continue to get larger forever. Now, there are several keys features we should notice about this function. Try graphing y=sqrt(x) on Desmos to see how this looks like. But, if we now swap variables, we will get the same graph as before but now the graph will oriented differently. Now, the graph will look the same as before, but x is the independent variable. Notice that if we want to make x the independent variable, we can easily do so by taking the square root of both sides (x=sqrt(y)). Visualize a squared function in your head (y=x^2), but only in the first quadrant.
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