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. Stretched vertically, compressed vertically, stretched horizontally, shifts left, shifts right, and reflections across. In this form a represents vertical stretches and compressions and the k represents horizontal stretches and compressions. Doing stretches, compressions and reflections horizontally are different types of transformations of functions. Each of the following functions represents a vertical stretch or squeeze of a simpler basic function. 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. Scroll down the page for more examples, solutions and explanations. 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.
Investigating horizontal stretches compressions and reflections. Transform the given function fx as described and write the resulting function as an equation. Horizontal and vertical graph stretches and compressions part. Use the graph of a basic function and a combination of transformations to sketch the functions. Part 1 the general formula is given as well as a few concrete examples. Go to calculator for graphing demonstrations the rest of class. For example, if we begin by graphing the parent function f x 2x, we can then graph the stretch, using a 3. Write the equation of the original function in each case. The freezing point of water is 0c and 32f, while the boiling point is 100c and 212f. The picture of the butterfly has been stretched enlarged and shrunk. 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.
Now, to vertically compress this curve, you put a fraction coefficient in front of the x component of. 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. Calculus 1 functions in this video, we learn an algebraic way to stretch, compress, and reflect the graphs of functions. Transformations of functions chandlergilbert community. Horizontal and vertical graph stretches and compressions. Stretches and compressions of functions graphs can be stretched elongated or compressed squeezed both vertically and horizontally. Horizontal and vertical stretches and compressions quizlet. Start studying lesson transforming linear functionsstretches and compressions lesson 21 transforming to graph quadratic functions.
Sketch graphs by applying a reflection in the yaxis, andor a horizontal stretch or compression to a known graph of a function. An introduction to graph compression techniques for inmemory graph computation 3 a scheduler, and update functions. A vertical scaling multipliesdivides every ycoordinate by a constant while leaving the xcoordinate unchanged. Throughout, you will use the same function fx that you used in the previous activity.
Now, to vertically compress this curve, you put a fraction coefficient in front of the x. Function stretch and compression will be the subject of these interactive study resources. We will now begin to study what happens when we multiply the. The xvalues, or input, of the function go on the xaxis of the graph, and the fx values also called yvalues, or output.
Shifting, reflecting and stretching graphs we begin this lesson with a summary of common graphs that we have seen thus far. 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. Nevertheless, these are very common functions and it is. Describe the transformations necessary to transform the graph of f x into that of gx. How a graph is transformed is determined by the way certain numbers, called parameters, are. Reflections we have studied how adding or subtracting constants to the inside or outside of a function affects its graph. Reflections and horizontal and vertical stretches and compressions activity 3. In other words, compared to pregel, there are no messages passed from vertices. Transformations must be performed in the following order.
The exercises in this lesson duplicate those in graphing tools. Transformations of trigonometric graphs videos, worksheets, solutions, and activities to help precalculus students learn about horizontal and vertical graph stretches and compressions. You can apply the four types of transformationsstretches, compressions, reflections, and translationsto logarithmic functions. Just like transformations in geometry, we can move and resize the graphs of functions. 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. In addition to shifting, compressing, and stretching a graph, we can also reflect it about the xaxis or the yaxis. This video looks at how a and b affect the graph of fx. Horizontal and vertical stretches and compressions this video explains how to graph horizontal and vertical stretches and compressions in the form a. Graph transformations horizontal and vertical graph stretches and compressions. Identify the domain and range of a function, after a horizontal stretch or compression andor reflection in the yaxis. Amplitude, period, vertical and horizontal shifts, ex 2. How a graph is transformed is determined by the way certain numbers, called parameters, are introduced in the function.
Aug 12, 2008 graph transformations horizontal and vertical graph stretches and compressions. You can apply the four types of transformationsstretches, compressions, reflections, and translationsto exponential functions. Stretching graphs and compressing graphs the numerist. 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. 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. 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. Test questions will cover points of interest like stretching a 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.
In this form a represents vertical stretches and compressions and the k. Notes,whiteboard,whiteboard page,notebook software,notebook,pdf,smart,smart technologies ulc,smart board interactive whiteboard created date. Scales stretch compress a scale is a nonrigid translation in that it does alter the shape and size of the graph of the function. Identifying horizontal squash from graph video khan academy. We can stretch or compress it in the ydirection by multiplying the whole function by a constant. Functions stretching, compressing, and reflecting functions.
We can stretch or compress it in the ydirection by multiplying the whole. In this video from patrickjmt we discuss horizontal stretching and compressing of graphs. Students are given a table of values for a function and asked to complete the table with values of stretches and compressions. For example, 2, 0 and 2, 0 are invariant points for the graph and its transformation below. When we multiply the parent function latexf\leftx\rightbxlatex by 1, we get a reflection about the xaxis. Stretching graphs and compressing graphs math concepts. 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. Use transformations of a parent function to sketch the graphs of. The general formula is given as well as a few concrete examples. Stretching and compressing functions or graphs examples. 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. The following table gives a summary of the transformation rules for graphs. If the constant is greater than 1, we get a vertical stretch. Stretching graphs and compressing graphs if you understand how to shift a curve horizontally or vertically, stretching graphs or compressing them isnt much different.
Stretching and shrinking graphs of functions engageny. Horizontal and vertical shifts compressions and stretches. This tells us that we need to multiply each of the coordinates on the graph by in order to stretch the original graph example. 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. If is transformed to, where a is a number, describe the transformation. Stretching, compressing, or reflecting an exponential. Vertical translations a shift may be referred to as a translation. 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. Investigating stretches and compressions let, where a is the parameter. We can now add to the general form of all functions. We have already had experience with constant and linear functions, and have been introduced, albeit sparingly, to the other graphs. Construct understanding look at the following graphs.
Find the equation of a line that is perpendicular to the line 4 and passes through the point 3,11. Lesson transforming linear functionsstretches and. If c is multiplied to the function then the graph of the function will undergo a vertical stretching or compression. Start studying horizontal and vertical stretches and compressions. Investigating translations complete the following given the graph of fx. Note that unlike for the ydirection, bigger values cause more compression. A vertical stretch or compression results from multiplying the outside of a function by a constant k. Once again, its only a small modification to the equation that causes the stretch or compression. 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. Essential understanding teks 5a determine the effects on the key attributes on the graphs of fx bx and fx.
Graph functions using compressions and stretches college. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Horizontal stretches, compressions, and reflections lesson 4 mhf4uc myilc. We will begin this exploration of linear functions with a look at graphs. Apr 12, 2019 what are the effects on the parent function when. Example one for each pair of functions, identify the parent function. Stretches and compressions of graphs stretches of graphs. Is it possible to shrink or stretch the graph of a function.