That is, you should be familiar with them, but it's worth the time at the outset to make sure we're familiar with these different functions that we're going to use in this session. To begin with, let's review some functions that you should already have at your beck and call. We'll look at reflections, compressions and stretches, and then combinations of transformations. We'll look at vertical and horizontal shifts. Now, in particular, we're going to look at some specific types of transformations you can do on functions in order to change their graphs. During this session, we're going to look at a topic called transformations. ĭo you need more help? Please post your question on ourĬopyright © 1999-2023 MathMedics, LLC. Solving an equation from a graph: Example. Example.Ĭombination of stretch, shrink, reflection, horizontal, and vertical shifts: Example. Stretch and Shrink: The graph of f(x) versus the graph of f(Cx). Stretch and Shrink: The graph of f(x) versus the graph of C(x). Horizontal shifts: The graph of f(x) versus the graph of f(x + C) Example.Ĭombination horizontal shift and reflection across the y-axis: The graph of f(x) versus the graph of f(- x + C) or f(C - x) Example.Ĭombination horizontal and vertical shifts: The graph of f(x) versus the graph of f(x + A) + B Example.Ĭombination horizontal and vertical shifts and reflections: The graph of f(x) versus the graphs of -f(x) + C. Vertical shifts: The graph of f(x) versus the graph of f(x) + C. Reflection over the y-axis: The graph of f(x) versus the graph of f(-x). If you would like to review examples on the following, click on Example: Since the point (1, 0) is on the x-axis, the point would not move. , it would be shifted up 22 units to (b, 11). If the point (b, -11) is located on the graph of If we shifted the point (a, 8) down 16 units, it would wind up at (a, - 8) units. For example, the point (a, 8) is located 8 units up from the x-axis. Every point on the graph of would be shifted up or down twice it’s distance from the x-axis. Fold the graph of over the x-axis so that it would be superimposed on the graph of.The graph of is a reflection over the x-axis of the graph of. What exactly does that mean? Well for one thing, it means if there is a point (a, b) on the graph of, we know that the point (a, - b) is located on the graph of. This means both graphs are symmetric to each other with respect to the x-axis. Note that the graph of the function is superimposed on the graph of the function. Mentally fold the coordinate system at the x-axis.Note that both points have the same x-coordinate and the y-coordinate’s differ by a minus sign.Since neither of the graphs cross the y-axis, there is no y-intercept. ![]() The graphs of both functions cross the x-axis at x = 1.This verifies that the domain of both functions is the set of positive real numbers. You can see that the graphs of both functions are located in quadrants I and IV to the right of the y-axis.The domain of both functions is the set of positive real numbers.The graph to the right of the y-axis is the graph of the function, and the graph on the left to the left of the y-axis is the graph of the function. ![]()
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