Investigating translations complete the following given the graph of fx. Students are given a table of values for a function and asked to complete the table with values of stretches and compressions. Nevertheless, these are very common functions and it is. Go to calculator for graphing demonstrations the rest of class. Horizontal and vertical graph stretches and compressions. Vertical translations a shift may be referred to as a translation. Construct understanding look at the following graphs. If c is multiplied to the function then the graph of the function will undergo a vertical stretching or compression. Horizontal stretches, compressions, and reflections lesson 4 mhf4uc myilc. You saw that the vertical stretches and shrinks changed the amplitude of sine and cosine graphs, but did not change the midline on the xaxis, and the horizontal stretches and compressions changed the period of all of the graphs. Changes in amplitude are vertical stretches or shrinkscompressions changes in period are horizontal stretches or shrinkscompressions phase shifts are horizontal left or right shifts these graphs can also be shifted vertically, but that isnt shown in all classes. Stretching graphs and compressing graphs if you understand how to shift a curve horizontally or vertically, stretching graphs or compressing them isnt much different.
If is transformed to, where a is a number, describe the transformation. This tells us that we need to multiply each of the coordinates on the graph by in order to stretch the original graph example. Essential understanding teks 5a determine the effects on the key attributes on the graphs of fx bx and fx. Stretches and compressions of functions graphs can be stretched elongated or compressed squeezed both vertically and horizontally. An introduction to graph compression techniques for inmemory graph computation 3 a scheduler, and update functions. This video looks at how a and b affect the graph of fx.
Find the equation of a line that is perpendicular to the line 4 and passes through the point 3,11. In other words, compared to pregel, there are no messages passed from vertices. You can apply the four types of transformationsstretches, compressions, reflections, and translationsto logarithmic functions. Stretching, compressing, or reflecting an exponential. Stretching graphs and compressing graphs the numerist. A scale will multiplydivide coordinates and this will change the appearance as well as the location. Investigating stretches and compressions of function graphs in this activity, you will consider what happens when you multiply by a positive parameter inside or outside a function. Throughout, you will use the same function fx that you used in the previous activity. A vertical stretch or compression results from multiplying the outside of a function by a constant k.
We can stretch or compress it in the ydirection by multiplying the whole function by a constant. Horizontal and vertical stretches and compressions this video explains how to graph horizontal and vertical stretches and compressions in the form a. Stretching and compressing graphs vertically is determined by the coefficient in front of the x or more specifically, in front of the other direct modifications to x. Stretching graphs and compressing graphs math concepts. We have already had experience with constant and linear functions, and have been introduced, albeit sparingly, to the other graphs. Identifying horizontal squash from graph video khan academy. Note that unlike for the ydirection, bigger values cause more compression. Once again, its only a small modification to the equation that causes the stretch or compression. Reflections and horizontal and vertical stretches and compressions activity 3.
Apr 12, 2019 what are the effects on the parent function when. Doing stretches, compressions and reflections horizontally are different types of transformations of functions. Amplitude, period, vertical and horizontal shifts, ex 2. Graph functions using compressions and stretches college. Part 1 the general formula is given as well as a few concrete examples. The xvalues, or input, of the function go on the xaxis of the graph, and the fx values also called yvalues, or output. The following table gives a summary of the transformation rules for graphs. Stretches and compressions of graphs stretches of graphs. Graph functions using compressions and stretches adding a constant to the inputs or outputs of a function changed the position of a graph with respect to the axes, but it did not affect the shape of a graph. Transform the given function fx as described and write the resulting function as an equation. Scroll down the page for more examples, solutions and explanations. Test questions will cover points of interest like stretching a function. For example, 2, 0 and 2, 0 are invariant points for the graph and its transformation below. To perform a horizontal compression or stretch on a graph, instead of solving your equation for fx, you solve it for fcx for stretching or fxc for compressing, where c is the stretch factor.
When we multiply a function by a positive constant, we get a function whose graph is stretched or compressed vertically in relation to the graph of the original function. The simplest way to consider this is that for every x you want to put into your equation, you must modify x before actually doing the substitution. Identify the domain and range of a function, after a horizontal stretch or compression andor reflection in the yaxis. How a graph is transformed is determined by the way certain numbers, called parameters, are introduced in the function. Use transformations of a parent function to sketch the graphs of. Graph transformations horizontal and vertical graph stretches and compressions. Example one for each pair of functions, identify the parent function. Given the graphs of functions f and g, where g is the result of compressing f by a factor of 2, sal finds gx in terms of fx. Start studying horizontal and vertical stretches and compressions. Stretched vertically, compressed vertically, stretched horizontally, shifts left, shifts right, and reflections across. Start studying lesson transforming linear functionsstretches and compressions lesson 21 transforming to graph quadratic functions. Describe the transformations necessary to transform the graph of f x into that of gx.
They are then asked to graph the original function and compare it to the transformed functions graphs and to describe the relationship between the original. Transformations of functions chandlergilbert community. Stretching and compressing functions or graphs examples. We can stretch or compress it in the ydirection by multiplying the whole. Use the graph of a basic function and a combination of transformations to sketch the functions. Jun 03, 2007 stretching graphs and compressing graphs if you understand how to shift a curve horizontally or vertically, stretching graphs or compressing them isnt much different. Functions stretching, compressing, and reflecting functions.
How a graph is transformed is determined by the way certain numbers, called parameters, are. Graphical transformations of functions in this section we will discuss how the graph of a function may be transformed either by shifting, stretching or compressing, or reflection. Sketch graphs by applying a reflection in the yaxis, andor a horizontal stretch or compression to a known graph of a function. Horizontal and vertical graph stretches and compressions part 2 of 3 horizontal and vertical graph transformations trigonometric functions and graphing. Is it possible to shrink or stretch the graph of a function. Transformations of trigonometric graphs videos, worksheets, solutions, and activities to help precalculus students learn about horizontal and vertical graph stretches and compressions. In addition to shifting, compressing, and stretching a graph, we can also reflect it about the xaxis or the yaxis. Transformations must be performed in the following order. Function stretch and compression will be the subject of these interactive study resources. Scales stretch compress a scale is a nonrigid translation in that it does alter the shape and size of the graph of the function. For example, if we begin by graphing the parent function f x 2x, we can then graph the stretch, using a 3. The picture of the butterfly has been stretched enlarged and shrunk. In this video from patrickjmt we discuss horizontal stretching and compressing of graphs. Shifting, reflecting and stretching graphs we begin this lesson with a summary of common graphs that we have seen thus far.
Stretched vertically, compressed vertically, stretched horizontally, shifts left, shifts right, and reflections across the x and y axes, compressed horizontally precalculus, examples and step by step solutions, function transformations. Just like transformations in geometry, we can move and resize the graphs of functions. Now, to vertically compress this curve, you put a fraction coefficient in front of the x component of. Reflections we have studied how adding or subtracting constants to the inside or outside of a function affects its graph. Each of the following functions represents a vertical stretch or squeeze of a simpler basic function. Horizontal and vertical shifts compressions and stretches. We will begin this exploration of linear functions with a look at graphs. You can apply the four types of transformationsstretches, compressions, reflections, and translationsto exponential functions. Investigating stretches and compressions let, where a is the parameter. We will now begin to study what happens when we multiply the. Write the equation of the original function in each case. Notes,whiteboard,whiteboard page,notebook software,notebook,pdf,smart,smart technologies ulc,smart board interactive whiteboard created date. Lesson transforming linear functionsstretches and. The exercises in this lesson duplicate those in graphing tools.
When we multiply the parent function latexf\leftx\rightbxlatex by 1, we get a reflection about the xaxis. To make the students to understand the stuff horizontal stretches, compressions and reflections, we have explained the rule that we have to apply to make horizontal stretch, compression and reflection in a function. While horizontal and vertical shifts involve adding constants to the input or to the function itself, a stretch or compression occurs when we multiply the parent function f x bx by a constant a 0. In this form a represents vertical stretches and compressions and the k. The general formula is given as well as a few concrete examples. Horizontal and vertical graph stretches and compressions part.
Stretching and shrinking graphs of functions engageny. A vertical scaling multipliesdivides every ycoordinate by a constant while leaving the xcoordinate unchanged. Investigating horizontal stretches compressions and reflections. Horizontal and vertical stretches and compressions quizlet. The freezing point of water is 0c and 32f, while the boiling point is 100c and 212f. Calculus 1 functions in this video, we learn an algebraic way to stretch, compress, and reflect the graphs of functions. Now, to vertically compress this curve, you put a fraction coefficient in front of the x. In this form a represents vertical stretches and compressions and the k represents horizontal stretches and compressions.
Aug 12, 2008 graph transformations horizontal and vertical graph stretches and compressions. We can now add to the general form of all functions. If the constant is greater than 1, we get a vertical stretch. Learn vocabulary, terms, and more with flashcards, games, and other study tools.
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