(There are word and PDF copies of each - one with the GCSE stuff on only and one with A level stuff as well). I tried copying them into an A5 booklet to save money on photocopying but to be honest the quality isn’t good and they are too small - if using probably go the whole hog and print as an A4 booklet. I have included worksheets which include blanks of the graphs used as well as the questions and summary table. Many of these are included later on along with stretches. If teaching A level, omit slides 16 to 24 which are questions but these only include work on translations and reflections. Of course if you wish to stretch your GCSE group and expose them to some A level work, feel free to continue. If teaching GCSE I suggest stopping at slide 24. It develops into multiple transformations and the effects on coordinates as well as sketching graphs which have under-gone transformations. The powerpoint takes the student through the two translations and two reflections (as far as you need to go for GCSE) and then the two stretches (A level but if you want to stretch some of your able GCSE students and give them a taste of A level, you can include this as part of your GCSE teaching also).Īlso included are links to a desmos file which models these transformations and can be used to show the effect with various constants. A function can be compressed or stretched vertically by multiplying the output by a constant.This resources is designed to deliver the transformation of graphs for the GCSE higher tier course and the A level course.A function can be odd, even, or neither.Odd functions satisfy the condition f\left(x\right)=-f\left(-x\right).Even functions satisfy the condition f\left(x\right)=f\left(-x\right).Vertical shift by k=1 of the cube root function f\left(x\right)=\sqrt axis, whereas odd functions are symmetric about the origin. For a function g\left(x\right)=f\left(x\right) k, the function f\left(x\right) is shifted vertically k units.įigure 2. A vertical reflection reflects a graph vertically across the x-axis, while a horizontal reflection reflects a graph horizontally across the y-axis. ANSWER: reflection and translation (glide. The resulting transformation can also be called a glide reflection. Another transformation that can be applied to a function is a reflection over the x or y-axis. Step 2:Translate the triangle to the right. In other words, we add the same constant to the output value of the function regardless of the input. Graphing Functions Using Reflections about the Axes. The simplest shift is a vertical shift, moving the graph up or down, because this transformation involves adding a positive or negative constant to the function. One simple kind of transformation involves shifting the entire graph of a function up, down, right, or left. There are systematic ways to alter functions to construct appropriate models for the problems we are trying to solve. One method we can employ is to adapt the basic graphs of the toolkit functions to build new models for a given scenario. Often when given a problem, we try to model the scenario using mathematics in the form of words, tables, graphs, and equations. Graphing Functions Using Vertical and Horizontal Shifts Another transformation that can be applied to a function is a reflection over the x- or y-axis. In this section, we will take a look at several kinds of transformations. Graphing Functions Using Reflections about the Axes. In a similar way, we can distort or transform mathematical functions to better adapt them to describing objects or processes in the real world. When we multiply the input by 1, we get a reflection about the y -axis. When we multiply the parent function f (x) bx f ( x) b x by 1, we get a reflection about the x -axis. Look at the grid below, which is an example of. A transformation is a way of changing the position (and sometimes the size) of a shape. But what happens when we bend a flexible mirror? Like a carnival funhouse mirror, it presents us with a distorted image of ourselves, stretched or compressed horizontally or vertically. Graphing Reflections In addition to shifting, compressing, and stretching a graph, we can also reflect it about the x -axis or the y -axis. Translations and reflections are examples of transformations. When we tilt the mirror, the images we see may shift horizontally or vertically. We all know that a flat mirror enables us to see an accurate image of ourselves and whatever is behind us.
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