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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

Harvey Mudd College

Baylor University

Idaho State University

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 $y=|x-…

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Sketch the graph of the eq…

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Sketch the graph of $y=|2 …

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Sketch a graph of the equa…

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Sketch the graph of $y=2 /…

So this problem we're going to sketch the graph of why equals the absolute value of X plus two now graph apiece graph an absolute value function. It's often good to break it into a piece wise function because we have two very distinct things that we're looking at. If what's inside thes absolute value bars is positive, then the value is if the piece wise function is just what's inside those absolute value bars. However, if what's inside is negative, then the value of the function is actually the opposite of what's inside there because the absolute value bars will switch the sign. So let's take a look at what we have in here. We have X Plus two, So let's see where it changes from being positive to negative. Where is X plus two greater than or equal to zero? Well, if I subtract two that gives me X is greater than or equal to negative two. So if X is greater than or equal to negative two than the value of my function is X plus to the absolute value, bars change nothing. However, if X is smaller than that, if X is less than negative too then what's inside is negative. And I have to switch the sign so it becomes negative. X minus two. Every term is has to be negated. So now we have two different equations that weaken graph on our chart. Let's do the first one. Why equals negative X minus two? Well, that is our slope intercept form. So our slope is negative. One in our intercept is negative two. So there's a there's my negative to for my intercept. However, my graph doesn't actually begin. Their this piece doesn't start till X is less than negative too. So as I draw in a line with a negative one slope, I'm just going to start it off with a little bit of a dotted line on Lee when it gets to X equal in two. Um, I going to start this line solid. That dotted line was just to help me graph. It's not really part of this, uh, graph of this function. Now, let's look at our second piece. Why equals positive X plus two. So if I have, um, again, this gives me an intercept of positive too, right up there and a slope of one. So it goes that way, and it's gonna come this direction until I get two. X equals negative, too, because that's where that piece begins. As you can see both pieces meat right there at X equal in two. And why is zero that gives us a very classic V shape that you see a lot with absolute value markings? Um, because we often could make it into a piece wise function. So the V has one piece going one direction, one piece going to the other, and they often meet at a sharp point just like this one did here.

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