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Sketch the graph of $y=|x-2|$.

Algebra

Chapter 1

Functions and their Applications

Section 2

Basic Notions of Functions

Functions

Campbell University

Baylor University

University of Michigan - Ann Arbor

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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Sketch the graph of the eq…

02:57

Sketch the graph of $y=|x+…

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03:14

Sketch the graph of $y=|2 …

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00:54

Sketch the graph.$$x=y…

for this problem, we're going to sketch the graph. Why equals the absolute value of X minus two? Now a good way to graph absolute value functions is to break it up into a piece wise function because there are two different ways that we could evaluate this. If what's inside the absolute value bars is positive, the absolute value bars really don't mean anything. It's just gonna be exactly whatever is there. If what's inside those bars is negative, then we take the opposite. So let's look at what's inside our absolute value. Bars X minus two. Where is that greater than or equal to zero? Well, solving it for X. It's when X is greater than or equal to two. So if X is greater than or equal to two, what's inside The absolute value bars is positive, and the value is X minus two. If X is less than two, though, then what's inside those absolute value bars is negative, and I have to take the opposite. That becomes negative X plus two. So let's graph each of these independently. First, why equals negative X plus two? Well, that has a slope of negative one and a white intercept of to. So there's two and it has a slope of negative one. And this line is going to go all the way to the point where X equals two. So it's gonna come all the way down to right there. Now what about our other line? Why equals X minus two? Well, that has an intercept of negative, too. And I'm going to just sketch that in here just a little bit, and it has a slope of one, but it really Onley begins when X is too. So knowing that that's where it begins, I just put that little dotted line in. It's not technically part of the graph, but it shows you, um, you know that it all fits in here. It shows you where it starts and gets the right angle going, and they do meet right there. At that point, X equals two right where we had that change for our piece wise function. This is a very classic shape for an absolute value function. You often see that V shape where it switches from one piece of the piece wise function to the other

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