Graph the following functions and state their domain and range. We should always take care of the stretching or shrinking and reflections first. When a functiongraph is reflected in a line, everything on one side of the line is flipped over. Work with your group members to answer the following questions. A vertical translation is a rigid transformation that shifts a graph up or down relative. Identifying function transformations video khan academy. A translation in which the graph of a function is mirrored about an axis. Using transformations to graph functions mathematics. Graph each function using the techniques of shifting. These examples represent the three main transformations. The graph of y x2 is the reflection of the graph of y x2 in the xaxis. Students will understand how to identify transformations of graphs and in what order. Shift graphs left, right, up, down reflect graphs across the x or y axis stretch graphs or shrink you may also look at a graph and be asked to explain what happened to the original graph. Learn how to recognize shifts, vertical and horizontal stretches and reflections as they affect parent functions in this free math video tutorial by marios math tutoring.
Maths made easy gives you access to maths worksheets, practice questions and. Start with the graph of the basic function and show all stages. You can move the graph of a linear function around the coordinate grid using transformations. Scale a translation in which the size and shape of the graph of a function is changed. Shifting, stretching and reflecting parent function graphs. The function g is steeper than the basic squaring function and its graph appears to have been stretched vertically. Start with graph of the basic function shown to the right. Conversely, students will be able to create graphs from basic functions using the. Stretches compressions translations shifts reflections chandler. Start with the graph of the basic function for example, y x2. The x coordinates are unaffected but all the y coordinates are flipped. Graph the following function using the techniques of shifting, compressing, stretching andor reflecting.
Graph transformations worksheets questions and revision mme. These transformations can be performed in both the x and y directions. Reflection over xaxishorizontal shift left 6 unitsvertical shift upward 7 units 31. Graph the following function using the techniques of shifting. Reflections in the coordinate axes of the graph of y f x are represented as follows. The x coordinates are unaffected but all the y coordinates go down by 3. Graphical transformations of functions miami arts charter school. Sal walks through several examples of how to write gx implicitly in terms of fx when gx is a shift or a reflection of fx. Tes global ltd is registered in england company no 02017289 with its registered office. September 15, 2010 the figure shows a graph of y x 3. Shifting reflecting and stretching graphs activity. The x coordinates are unaffected but all the y coordinates are doubled. In this lesson you learned how to identify and graph shifts, reflections, and nonrigid transformations of functions.
Reflections are isometric, but do not preserve orientation. Graph functions by stretching or compressing basic functions. From the examples of vertical shifts above, you might think that the graph of gx is the graph of fx, shifted. When a functiongraph is translated, it is shifted leftright, updown, or some combination of the two. Graph each function using the techniques of shifting, compressing, stretching, andor reflecting.
Transformations must be performed in the following order. In this section we will discuss how the graph of a function may be transformed either by shifting, stretching or compressing, or reflection. This website and its content is subject to our terms and conditions. Activity 4 graph each of the functions on the same graph. Graph functions that are reflections of basic functions. Start by graphing y 2x by plotting at least 3 points.