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a. Draw the graphs of $y=-|x-4|$ and $y=-2$b. From the graph drawn in a, determine the solution set of $-|x-4|=-2$c. From the graph drawn in a, determine the solution set of $-|x-4| > -2$d. From the graph drawn in a, determine the solution set of $-|x-4| < -2$

a) See graphb) $\{2,6\}$c) $\{x : 2<x<6\}$d) $\{x : x<2 \text { or } x>6\}$

Algebra

Chapter 4

RELATIONS AND FUNCTIONS

Section 4

Absolute Value Functions

An Introduction to Geometry

Functions

Linear Functions

Polynomials

Missouri State University

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

01:11

04:13

Draw a graph of $y=x^{2}-4…

02:27

Solve the given equation o…

05:17

a. Graph the solution set …

02:18

? Solving Equations and In…

04:54

CHALLENGE Graph each set o…

04:38

Graphing the Absolute Valu…

00:54

Match the graph with the s…

00:42

01:51

02:41

(a) use a graphing utility…

So for this exercise where we are going to want to start by graphing the equations y equals negative, absolute value of X minus four. And why equals and negative too. Okay, so first thing I'm gonna do is draw on this negative to graph. That's pretty simple. That's just going to be a vertical. I'm sorry. Horizontal line at y equals negative, too. And then, for this next graph I am going to plug in, we're gonna plug in four for our X value. So if we put in four for X value, we see that are y value is going to be zero. And if we plug in 34 I was spoken to for our X value. We see that to minus four is negative to absolute value of negative to positive, too. But we have that negative symbol out in front. So that means that our output is actually going to be negative too. So I'm gonna connect these two points right here. So now we have our two graphs. Okay, So the second part of the question asks us to determine the solution set of the equation. Negative. X minus four equals negative, too. So Essentially, what this is asking for is where the two graphs overlap. And we see that thesis a Lucian to that is X equals positive, too. So the solution said here is X equals two. Because if we plug in to for X, we get to minus four negative to absolute values. Positive to negative symbol outside makes it negative, too. Negative too, is equal in negative too. All right. For the next part of the question, we, ah, need to determine the solution set too. Absolute value of X minus four is greater than negative, too. So if we look at our graph, we see that the values that make this expression greater than negative too are all of the ex valuable. All of the essentially, we want to find the region of the graph that satisfies this expression. So, uh, any value for X above this line and this line is going to satisfy this equation. So our region is everything right here, because if we plugged in, yeah, anyways, do, do, do, do do. And now we want to find the solution region for the expression negative. X minus four is less than they give to. So that is going to be everything in this region right here, because these are all of the values that make our output come out to less than negative, too.

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