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Sketch the graph of $y=|2 x-3|$.

Algebra

Chapter 1

Functions and their Applications

Section 2

Basic Notions of Functions

Functions

Missouri State University

Oregon State University

McMaster 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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Draw the graph of y=-2…

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Sketch the graph of the eq…

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Sketch the graph of $y=|x-…

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Sketch the graph of $y=|x+…

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Sketch a graph of the equa…

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01:57

for this problem, we're going to sketch the graph of why equals the absolute value of two X minus three. Now, anytime we have an absolute value function, it's often easiest to graph if we break it up into a piece wise function because we have two very distinct things going on with an absolute value function. If what's inside Thebes salute value markings is positive or zero, the functions just equal to whatever that is. The absolute value bars make no difference to the value of the function. However, if what's inside those bars is negative, then I have to take the opposite sign. So if it's a negative, three would have to take the opposite of that or positive three. So it's important to figure out what makes that positive and what makes it negative. So let's take what's inside our bars there two X minus three, and I want to see where is it greater than or equal to zero. So if I solve this for X, that gives me a value of X greater than or equal to three halfs. So if X is greater than or equal to three halves than the value of the function is exactly what you see inside those absolute value bars. It's positive or zero. It doesn't change, however, for the other values of X. If X is less than three halves, then what's inside those absolute value bars is negative, and I need to take the opposite of it. So I take the opposite of each term. So negative two X plus three. So that's my piece wise function. Now let's see if we can graph it. Let's start with the first piece. Why equals negative two X plus three. Well, this is ah, line in slope intercept form. The slope is negative to the Y. Intercept is three. So if I put that here, why intercept just three and I have a slope of negative too, so negative to negative two. However, I need to be careful because this has a limited domain. It on Lee goes through X equaling three halves, which I'm gonna mark right there on my X axis. So these points, I will connect, but not the ones down on the bottom. Okay, that's not actually part of this graph. Just the pieces from X, equally three halves and smaller exes than that. Okay, What about our other piece? Y equals two X minus three. Well again, slope and intercept. So I have a slope of negative three. Alright. Sorry. Ah, Y intercept of negative three. And I have a slope of two. So I'm gonna put a couple of dots on here. But again, when I go to connect thes, I'm gonna Onley pick exes that air three halves or bigger. So I'm on Lee going to connect the dots here on the top portion. So the blue dots on the bottom you could ignore those were just a guide to help me graph what I have for my graph. Is that blue V? That's a very classic shape. You often see Avi, when you're graphing absolute value because you have this piece wise function. One half of the V comes from one piece of our function. Thea. Other half of the V comes from the other

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