Category: Kuta absolute value graphs

Graphing a shifted and stretched absolute value function

There are many opportunities for mistakes with absolute-value inequalities, so let's cover this topic slowly and look at some helpful pictures along the way. When we're done, I hope you will have a good picture in your head of what is going on, so you won't make some of the more common errors.

Once you catch on to how these inequalities work, this stuff really isn't so bad. Absolute Value Inequalities. This means that their absolute values will both be 2 ; that is, we have:. With this definition and picture in mind, let's look at some absolute value inequalities. This is an inequality. Where the solution to an absolute-value equation is points like in the graphic abovethe solution to an absolute-value inequality or "inequation" is going to be intervals.

In this inequality, they're asking me to find all the x -values that are less than three units away from zero in either directionso the solution is going to be the set of all the points that are less than three units away from zero. First, I'll draw a number line:. Looking at the inequality, I see that the number 1 will work as a solution, as will —1because each of these is less than three units from zero. The number 2 will work, as will —2. But 4 will not work, and neither will —4because they are too far away from zero.

Even 3 and —3 won't work though they're right on the edgebecause this is a "less than" but not equal to inequality.

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However, the number 2. In other words, all the points between —3 and 3but not actually including —3 or 3will work as solutions to this inequality. So, graphically, the solution looks like this:. The open circles at the ends of the blue line indicate "up to, but not including, these points. Translating this picture into algebraic symbols, I get the following solution:.

By the way, the correct conjunction for "less than" absolute-value inequalities is "and". Because the variable is contained within one interval. The x is in the interval that satisfied both inequalities at the same time. So "and" is the correct conjuction. Since this is a "less than" absolute-value inequality, my first step is to clear the absolute value according to the "less than" pattern.Test and Worksheet Generators for Math Teachers.

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kuta absolute value graphs

Stop searching. Create the worksheets you need with Infinite Algebra 2. Basics Order of operations Evaluating expressions Simplifying algebraic expressions. Linear Relations and Functions Review of linear equations Graphing absolute value functions Graphing linear inequalities. General Functions Evaluating functions Function operations Inverse functions. Equations and Inequalities Multi-step equations Work word problems Distance-rate-time word problems Mixture word problems Absolute value equations Multi-step inequalities Compound inequalities Absolute value inequalities.

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Shifting absolute value graphs. Practice: Shift absolute value graphs. Graphing absolute value functions. Practice: Graph absolute value functions. Absolute value graphs review. Next lesson. Current timeTotal duration Math: HSF.

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Google Classroom Facebook Twitter. Video transcript - [Instructor] So we're asked to graph f of x is equal to two times the absolute value of x plus three, plus two. And what they've already graphed for us, this right over here, this is the graph of y is equal to the absolute value of x.

So let's do this through a series of transformations. So the next thing I wanna graph, let's see if we can graph y. Y is equal is to the absolute value of x plus three. Now in previous videos we have talked about it. If you replace your x, with an x plus three, this is going to shift your graph to the left by three. You could view this as the same thing as y is equal to the absolute value of x minus negative three. And whatever you're subtracting from this x, that is how much you are shifting it.

So you're going to shift it three to the left. And we're gonna do that right now and then we're gonna just gonna confirm that it matches up. That it makes sense. So let's first graph that. Get my ruler tool here. So if we shift three to the left, it's gonna look something like It's gonna look something like this.

So on that When whatever we have inside the absolute value sign is positive, we're going to get essentially, this slope of one.

And whenever we have inside the absolute value sign is negative, we're gonna have a slope of essentially negative one. So it's going to look It's going to look like that.

Absolute Value Worksheets

And let's confirm whether this actually makes sense. Below x equals negative three, for x values less than negative three, what we're gonna have here, is this inside of the absolute value sign, is going to be negative and so then we're gonna take it's opposite value and so that makes sense. That's why you have this downward line right over here.

kuta absolute value graphs

Now for x is greater than negative three, when you add three to it, you're gonna get a positive value and so that's why you have this upward sloping line right over here.Our printable absolute value worksheets meticulously designed for 6th grade and 7th grade students include exercises like finding the absolute value of positive and negative integers, performing simple addition, subtraction, multiplication and division involving the absolute value of real numbers and more.

Begin your practice with our free worksheets. Find the absolute value of the integers.

Absolute-Value Inequalities

This stock of pdf worksheets featuring integers within offers the much-needed practice for 6th grade students. Simple Absolute Value 1. These printable handouts include questions on finding the absolute value of numbers with or without a negative sign. Challenging Absolute Value 1. Absolute Value Addition 1. Absolute Value Subtraction 1.

Add or Sub 1. Absolute Value Multiplication 1. Absolute Value Division 1. Multiply or Divide 1.

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With this set of printer-friendly worksheets, students are supposed to perform addition or subtraction or both the operations together on expressions involving the absolute value of numbers.

Evaluate the Value 1. This bunch of 7th grade worksheets tasks children to first evaluate the absolute value expressions and then multiply, divide and simplify them.

Multiplication and Division 1. Multiplication and Division 2. Multiplication and Division 3. Our mixed review pdf worksheets provide ultimate practice in performing all the four arithmetic operations on absolute value expressions.

Absolute Value Equation Calculator

Absolute Value Worksheet 1. Members have exclusive facilities to download an individual worksheet, or an entire level. Login Become a Member.This website uses cookies to ensure you get the best experience. By using this website, you agree to our Cookie Policy. Learn more Accept. Conic Sections Trigonometry.

Conic Sections. Matrices Vectors. Chemical Reactions Chemical Properties. Absolute Value Equation Calculator Solve absolute value equations step-by-step. Correct Answer :. Let's Try Again :. Try to further simplify. Solving absolute value equations is somewhat tricky; it requires understanding of the absolute value property Sign In Sign in with Office Sign in with Facebook. Join million happy users! Sign Up free of charge:.

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kuta absolute value graphs

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