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Use the points \(\{(−1, −2), (0, 0), (1, −2)\}\) to graph the reflected and dilated function \(y=−2|x|\). Then translate this graph \(5\) units to the right and \(3\) units down.
Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph. It's a common type of problem in algebra, specifically the modification of algebraic equations.
Here are some simple things we can do to move or scale it on the graph: We can move it up or down by adding a constant to the y-value: g(x) = x 2 + C. Note: to move the line down, we use a negative value for C. C > 0 moves it up; C < 0 moves it down We can move it left or right by adding a constant to the x-value: g(x) = (x+C) 2
• if k > 1, the graph of y = f (k•x) is the graph of f (x) horizontally shrunk (or compressed) by dividing each of its x-coordinates by k. • if 0 < k < 1 ( a fraction ), the graph is f ( x ) horizontally stretched by dividing each of its x -coordinates by k.
Starting at y=2f(x), click on the circle to reveal a new graph. Describe the transformation. Click again to remove and try the next function.
6 paź 2021 · OpenStax. Learning Objectives. Graph functions using vertical and horizontal shifts. Graph functions using reflections about the x-axis and the y-axis. Determine whether a function is even, odd, or neither from its graph. Graph functions using compressions and stretches. Combine transformations.
Translations (moving the whole graph in the x and/or y direction) Stretches (enlarging the graph but only in the x direction or only in the y direction) You should be able to recognise these three different methods of transforming graphs and be able to apply them to a given graph.
