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Problem 23 Medium 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 = \mid \sqrt{x} - 1 \mid $

Answer

$y=|\sqrt{x}-1|:$ Start with the graph of $y=\sqrt{x},$ shift it 1 unit downward, and then reflect the portion of the graph below the $x$ -axis about the $x$ -axis.

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Video Transcript

to graph dysfunction. Let's start by thinking about the standard function Y equals square root X. So a rough sketch of that would be something like this. It goes through 00 It goes through 11 It goes through four to Okay, what happens when we subtract one from it? That's going to shift the whole thing down one. So, what would that look like? Now, instead of going through 00 it goes through zero negative one. Instead of going through 11 it goes through 10 And instead of going through four to it goes through 41 shifted down one. Okay, now what happens when we take the absolute value of it? Well, the absolute value is going to make everything positive, so anything that was previously positive will still be positive. But anything that was negative is now going to be positive. So the part that was positive before was apart from X equals one on two. X equals four and beyond, so that's not going to change. So this part here his still is saying, But the other part down here, that was negative. We're going to reflect it across the X axis and make it positive. So we have this