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Problem 17 Easy Difficulty

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations.

$ y = 2 - \sqrt{x} $

Answer

$y=2-\sqrt{x}:$ Start with the graph of $y=\sqrt{x},$ reflect about the $x$ -axis, and then shift 2 units upward.

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Video Transcript

Our goal is to graft dysfunction, but we're going to start with the graph of one of the standard functions, which would be Weichel square root X. So it goes through 00 11 for two and it looks like this. That's the square root graft. Okay, so what do we want to do to it? We'll notice there's a negative sign in front of it, and so we want to multiply it by negative one. And what that's going to do is reflect the graph across the X axis so we could say casually flip it upside down. So now we're going to have 001 negative one for negative, too, which is flips the square root graph upside down. What happens now? We had to to get our final graph way out to and adding to to any graph is going to shift it up, too. So instead of having a point of 00 that point is now at zero to instead of having a point at one negative one that shifts up to as well. And instead of having a point of four negative to, that shifts up to a swell. So here's a graph