![]() ![]() ![]() And that's what the shifted graph shows.įor more on this, see the prior Dr. To check this, what will f(x + 1) be for x = 0? f(0 + 1) = f(1), which from the given graph is 1. (a) f(x + 1) will be a horizontal shift, 1 unit to the left: The first two cases are familiar to us now I made a rough sketch of the graph Pavan described, and did a shift for the first: Let's draw your graph like this: I am confused as to how I am supposed to plot f(abs(x)): even after I looked up its solution, I am unsure as to how they got that answer. I have to sketch the graphs of the functions To the left of the origin, it slowly tails off to negative infinity. Now we come to the really tricky case (but it’s really easy): \(f\left(\left|x\right|\right)\), from 2013: ABS(f(x)) and f(ABS(x)) GraphsĪ graph of f(x) has a hump up to y = 1 for x between 0 and 2. ![]() Absolute value on the inside: erase and duplicate I doubt that a teacher would assign this and expect perfection this question is more a matter of curiosity. It is above the red until the marked points where y = 1, and then is below the red. You’ll notice one feature I didn’t mention: Just as the graph of the absolute value approached the x-axis vertically at the origin, our blue graph approaches the x-axis vertically at each place where the original graph crosses the axis, even though the original was slanted there. Now, take our random function, and apply the square root to it: (In fact, what we are doing here is taking the square root of the blue graph, to make the red one!) ![]() This is what the absolute value will do to y when we apply it to a function. When x is less than 0, there is no y when x is between 0 and 1, y is greater than x when x is greater than 1, y is less than x. It is not a function, because two of the points lie on the same vertical line its domain is not but \), compared to the function \(y = x\): In my answer, I will be ignoring the details of Loralei’s given graph, because she has made some mistake in describing it as described it consists only of five points (two of the points given are identical) with no lines joining them. Could you please suggest to me how I could go about solving this problem? I have searched my text thoroughly for similar questions, and I have not had much luck. I have tried graphing this on my calculator as well, and I just don't understand how to shift, reflect, stretch, shrink or do whatever I'm supposed to do to this particular problem based on the shape of the base graph. Currently my base graph, if it were to be combined with the graph for y=|f(x)|, has a big X dissecting it at the origin. I have tried several methods to create the graph, and I know that I have missed or overlooked a key step somewhere. Is there any way I can find the answer by creating an overall equation for the base graph f(x) given the graphical information that I do have, such as the plotted points, domain, and range? In other words, given this information, can I reproduce or create what this absolute value graph should look like? Given that information, I'm fairly sure that the range is (-1,2). The following points are plotted on the graph: I need to give you a bit more information about the problem. However, when I try to sketch the graph for the following |f(x)|, I don't know how to graphically represent it. I am asked to sketch graphs of various equations such as y=f(x-2), y=f(x)-2, etc. Sketch the graph ofīasically, what I have is a grid, with the given function's graph. I'm currently enrolled in pre-calculus algebra, and I am stuck on the following problem: Absolute value on the outside: foldįirst, we have a question about the case \(\left|f(x)\right|\), from 2002: Graphing Absolute Values The first of these are the horizontal and vertical transformations introduced by absolute values (with a bonus thrown in: square roots) then next time we’ll conclude this series with a look at the special needs of trigonometric functions. Having looked at all the usual transformations of a function and its graph, there are two more situations I want to look at. ![]()
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