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# Y x absolute value graph

If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Donate Login Sign up Search for courses, skills, and videos. 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. 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.

### 3.6: Absolute Value Functions

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.

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So it's going to look It's going to look like that. And let's confirm whether this actually makes sense.Straight Lines Curvy Lines. Taking the absolute value of a negative number makes it positive. For this reason, graphs of absolute value functions tend not to look quite like the graphs of linear functions that you've already studied.

However, because of how absolute values behave, it is important to include negative inputs in your T-chart when graphing absolute-value functions. If you do not pick x -values that will put negatives inside the absolute value, you will usually mislead yourself as to what the graph looks like.

One of the other students does what is commonly done: he picks only positive x -values for his T-chart:. These points are fine, as far as they go, but they aren't enough; they don't give an accurate idea of what the graph should look like. In particular, they don't include any "minus" inputs, so it's easy to forget that those absolute-value bars mean something. As a result, the student forgets to take account of those bars, and draws an erroneous graph:.

But you're more careful. You remember that absolute-value graphs involve absolute values, and that absolute values affect "minus" inputs. So you pick x -values that put a "minus" inside the absolute value, and you choose quite a few more points. Your T-chart looks more like this:. While absolute-value graphs tend to look like the one above, with an "elbow" in the middle, this is not always the case.

However, if you see a graph with an elbow like this, you should expect that the graph's equation probably involves an absolute value.

In all cases, you should take care that you pick a good range of x -values, because three x -values right next to each other will almost certainly not give you anywhere near enough information to draw a valid picture. Note: The absolute-value bars make the entered values evaluate to being always non-negative that is, positive or zero.

As a result, the "V" in the above graph occurred where the sign on the inside was zero. When x equalled —2then the argument that is, the expression inside the bars equalled zero. For all x -values to the right of —2the argument was positive, so the absolute-value bars didn't change anything.

Noticing where the argument of the absolute-value bars will be zero can be helpful in ensuring that you're doing the graph correctly. In this case, only the x is inside the absolute-value bars. Also, since the "plus two" is outside of the absolute-value bars, I expect my graph to look like the regular absolute-value graph being a "V" with the elbow at the originbut moved upward by two units.The most significant feature of the absolute value graph is the corner point at which the graph changes direction.

This point is shown at the origin.

### Absolute value graph

The basic absolute value function changes direction at the origin, so this graph has been shifted to the right 3 units and down 2 units from the basic toolkit function. We also notice that the graph appears vertically stretched, because the width of the final graph on a horizontal line is not equal to 2 times the vertical distance from the corner to this line, as it would be for an unstretched absolute value function.

Instead, the width is equal to 1 times the vertical distance. Note that these equations are algebraically equivalent—the stretch for an absolute value function can be written interchangeably as a vertical or horizontal stretch or compression. Write the equation for the absolute value function that is horizontally shifted left 2 units, is vertically flipped, and vertically shifted up 3 units.

Do the graphs of absolute value functions always intersect the vertical axis? The horizontal axis? Yes, they always intersect the vertical axis. The graph of an absolute value function will intersect the vertical axis when the input is zero.

No, they do not always intersect the horizontal axis. The graph may or may not intersect the horizontal axis, depending on how the graph has been shifted and reflected. It is possible for the absolute value function to intersect the horizontal axis at zero, one, or two points.

Figure 8. Skip to main content. Absolute Value Functions. Search for:. Graph an absolute value function The most significant feature of the absolute value graph is the corner point at which the graph changes direction.

Figure 3. Figure 4.Username: Password: Register in one easy step! Reset your password if you forgot it. Algebra: Rational Functions, analyzing and graphing Section. Solvers Solvers. Lessons Lessons. Answers archive Answers. You can put this solution on YOUR website! Hi, Hope I can help. Absolute value is how far the number is on the number line.

Absolute value makes any number inside them positive. Knowing this principle. We know that "y" will always be positive, since "y" equals an absolute value.

All absolute value graphs look like a "V", the very point that the two lines meet will always be where "y" equals "0" since "0" is neither positive or negative, it doesn't have absolute valuethe "V" goes out from this point. Let us graph a few points. First we replace "x" with any number. We will replace "x" with Points are given as x,y.

Our point is -1,0. We need to find at least two more points to make the graph, we need a point with "x" as a positive number, and one with "x" as a negative number. We will replace "x" with "5". Our point is x,y5,6. We will now replace "x" with a negative number. We will replace "x" with.

Our point is x,y, We could now draw the equation, by drawing a line from -1,0 to11 then keep drawing the line after11then we would draw a line from -1,0 to 5,6 and beyond. We could find more points if we wanted to. Our point is -7,6. Our point is 10,The following steps will be useful to graph absolute value functions.

Step 1 :. Before graphing any absolute value function, first we have to graph the parent function :. If we plot these points on the graph sheet, we will get a graph as given below. When we look at the above graph, clearly the vertex is.

## Graphing absolute value functions

Write the given absolute value function as. To get the vertex of the absolute value function above, equate x - h and y - k to zero.

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That is. Therefore, the vertex is. According to the vertex, we have to shift the above graph. If we have negative sign in front of absolute sign, we have to flip the curve over.

So, the graph of the given absolute value function is. Example 2 :. Example 3 :. Subtract 3 from each side. Example 4 :.

Example 5 :. Example 6 :. Example 7 :. Because there is negative sign in front of the absolute sign, we have to flip the curve over. Example 8 :. Example 9 :. Hence, the graph of the given absolute value function is. Example 10 :. Example 11 :. Example 12 :.

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Solving quadratic equations by quadratic formula. Solving quadratic equations by completing square.An absolute value function is a function that contains an algebraic expression within absolute value symbols. Recall that the absolute value of a number is its distance from 0 on the number line. To graph an absolute value function, choose several values of x and find some ordered pairs. Also, if a is negative, then the graph opens downward, instead of upwards as usual.

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Absolute Value Functions An absolute value function is a function that contains an algebraic expression within absolute value symbols. Observe that the graph is V-shaped.

Also: The vertex of the graph is hk. Subjects Near Me. Louis Tutoring. Download our free learning tools apps and test prep books. Varsity Tutors does not have affiliation with universities mentioned on its website.In this mini-lesson, we will explore the world of Absolute Value Graph.

You can check out the interactive calculator to know more about the lesson and try your hand at solving a few interesting practice questions at the end of the page. In mathematics, functions play a very crucial role because it captures the relation between one quantity with the other. The graph of an absolute value function is called an absolute value graph. This is how the graph of absolute value function looks like.

The absolute value function is also called the modulus function. The function is defined for all real numbers. Experiment with the simulation below to observe the vertical shifts on the graph of the absolute value function.

Experiment with the simulation below to observe the horizontal shifts on the graph of the absolute value function.

No, Frank did not correctly plot the graph because the absolute value function takes into account the absolute values of numbers. So, let's take the same points we used for the previous example and change the sign of each number in the last row. Through an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic. The primary thing to remember while plotting graphs for absolute value inequality is that the graphs of absolute value are "V" shape.

Absolute value graph. Book a Free Class. The graph has an elbow in the middle as shown by Frank.

## Shifting absolute value graphs

So, let's start plotting these graphs. Lesson Plan 1. What Is an Absolute Value Graph? Solved Examples on Absolute Value Graph 3. Interactive Questions on Absolute Value Graph. How to Graph Absolute Value Functions? Let's plot the graph of the absolute value function. Important Notes. Solution No, Frank did not correctly plot the graph because the absolute value function takes into account the absolute values of numbers.

The function returns the non-negative values for every negative input. Let's a few negative integers and evaluate the value of the function at those points.

Can you plot the graph of this function? Hence, we have a graph of the signum function. Think Tank. How do you graph a double absolute value function? Follow the steps mentioned below to plot a graph of the double absolute value function. Separate cases of the function on which the function is defined.

For each domain, plot the graph of the function. How do you graph an absolute value inequality with two variables? Now we need to shade on side of this line.

Let's pick the point 0,0.