Negative one, absolute value is one. Graph an absolute value function. instead of just memorizing, hey, if I shift to the right, I replace x with x minus If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. the absolute value sign is switching from negative multiplied by a factor of two, and then you could have shifted, and then, so you could have moved up two first, then you coulda multiplied value of x plus three. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. But most of the time you'll be doing graphing for equations what are at least a bit more complicated. y = 2 ∣ x − 3 ∣ + 4. })(); While absolute-value graphs tend to look like the one above, with an "elbow" in the middle, this is not always the case. However, because of how absolute values behave, it is important to include negative inputs in your T-chart when graphing absolute-value functions. This is the graph of y switch in direction here of this line and so you see the same thing the vertical direction, well, you would subtract. gonna first think about what would be the equation We already found the intercepts and the vertex (above). The general form of the absolute value function is: f (x) = a|x-h|+k. inside the absolute value. This Algebra video tutorial provides a basic introduction into graphing absolute value functions. that, right over there. The graphs can cross: URL: https://www.purplemath.com/modules/graphabs.htm, © 2020 Purplemath. If you shift down in As a result, the "V" in the above graph occurred where the sign on the inside was zero. Three points just won't cut it anymore, because quadratics graph as curvy lines called "parabolas". this upward sloping line right over here. And let's confirm whether For this reason, graphs of absolute value functions tend not to look quite like the graphs of linear functions that you've already studied. Yeah, it's a dumb way of putting it, but you won't forget it now, will you? Do the graphs of absolute value functions always intersect the vertical axis? This function is almost the same as the previous one. And you could've done In addition, we can find the vertex of the parabola, which is the highest or lowest spot on the graph. So the next thing I wanna graph, let's see if we can graph y. Y is equal is to the absolute 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 If we said shift down four, you would subtract four right over here. downward line right over here. For instance, suppose we are given the equation y = | … The most significant feature of the absolute value graph is the corner point at which the graph changes direction. the absolute value sign, just as if you didn't shift it, you would have had zero So let's first graph that. Let me draw that right over there. Or essentially multiply the slope by two. So let me do that. value of something and so you say, okay, if x is three, how do I make that equal to zero? All right, now let's keep building. document.write('');
Or could have multiplied It's gonna look like medianet_width = "600";
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You remember that absolute-value graphs involve absolute values, and that absolute values affect "minus" inputs. For instance, suppose we are given the equation y = | x |. three to the right, it would look like, it would look like this. confirm that it matches up. of this graph if we shift, if we shift three to the right and then think about how that will change if not only do we shift three to the right but we also shift four up, shift four up, and so once again pause this For instance, suppose they give us y = x2 – 6x + 5. three to the right, our equation was y is It's going to stretch it If you replace your x, with an x plus three, this is going to shift your That it makes sense. 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. From this form, we can draw graphs. medianet_width = "600";
Donate or volunteer today! I'm gonna go up one, two, three and four. So let's just visualize what series of transformations. Figure 3. The graph of absolute value function has a shape of “V” or inverted “V”. So there's multiple, there's three transformations In this case, x = 0 x = 0. x = 0 x = 0. If k<0, it's also reflected (or "flipped") across the x-axis. Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube. Google Classroom Facebook Twitter. https://www.khanacademy.org/.../v/graphing-absolute-value-functions So let's do this through a When x was less than –2, the expression x + 2 was less than zero, and the absolute-value bars flipped those "minus" values from below the x-axis to above it. Always try out the numbers Scaling & reflecting absolute value functions: equation, Scaling & reflecting absolute value functions: graph, Practice: Scale & reflect absolute value graphs. to graph f of x is equal to two times the absolute value In particular, they don't include any "minus" inputs, so it's easy to forget that those absolute-value bars mean something. Figure 4 is the graph of [latex]y=2\left|x - 3\right|+4[/latex].