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When a horizontal shrink happens, the output values happen faster so our graph is compressed inward. On the bottom right we have a horizontal stretch. Our original function, f (x) - the red one, is narrower than the new function, f (c * x) - the green one. For the new functions to be wider, our c value needs to be 0 < c < 1.
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A horizontal stretching is the stretching of the graph away from the y-axis A horizontal compression (or shrinking) is the squeezing of the graph toward the y-axis. • 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.
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- Different Words Used to Talk About Transformations Involving YY and Xx
Points on the graph of y=f(x)y=f(x) are of the form (x,f(x)).(x,f(x)). Points on the graph of y=3f(x)y=3f(x) are of the form (x,3f(x)).(x,3f(x)). Thus, the graph of y=3f(x)y=3f(x) is found by takin...Points on the graph of y=f(x)y=f(x) are of the form (x,f(x)).(x,f(x)). Points on the graph of y=13f(x)y=13f(x) are of the form (x,13f(x)).(x,13f(x)). Thus, the graph of y=13f(x)y=13f(x) is found by...Transformations involving yywork the way you would expect them to work—they are intuitive.Here is the thought process you should use when you are given the graph of y=f(x)y=f(x) and asked about the graph of y=3f(x)y=3f(x):Points on the graph of y=f(x)y=f(x) are of the form (x,f(x)).(x,f(x)). Points on the graph of y=f(3x)y=f(3x) are of the form (x,f(3x)).(x,f(3x)).How can we locate these desired points (x,f(3x))(x,f(3x))? First, go to the point (3x,f(3x))(3x,f(3x)) on the graph of y=f(x).y=f(x). This point has the yy-value that we want, but it has the wrong...Transformations involving xx do NOT work the way you would expect them to work! They are counter-intuitive—they are against your intuition.Here is the thought process you should use when you are given the graph of y=f(x)y=f(x) and asked about the graph of y=f(3x)y=f(3x): original equation:y=f(x)new equation:y=f(3x)original equation:y=...Notice that different words are used when talking about transformations involving y,y, and transformations involving x.x. For transformations involving yy (that is, transformations that change the yy-valuesof the points), we say: DO THIS to the previous yy-value For transformations involving xx (that is, transformations that change the xx-valuesof ...
We can also stretch and shrink the graph of a function. To stretch or shrink the graph in the y direction, multiply or divide the output by a constant. 2f (x) is stretched in the y direction by a factor of 2, and f (x) is shrunk in the y direction by a factor of 2 (or stretched by a factor of ). Here are the graphs of y = f (x), y = 2f (x), and ...
Horizontal shrink is a geometric transformation that compresses or narrows a figure horizontally while leaving its vertical dimensions unchanged. It is also.
the horizontal compression will keep the new x-coordinate negative, but closer to the y-axis. Remember: The y-intercept value (where x = 0) stays attached to the y-axis, and does not change. A horizontal stretch "pushes" the graph horizontally closer to the y-axis (from the left and/or right). Given: f (x) = x 2 and k = 2. Horizontal Compression:
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What happens when a horizontal shrink happens?
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What is a vertical shrink on a graph?
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Does vertical stretching/shrinking change the Y Y value of a graph?
What is a horizontal shift?
Vertical Stretches and Compressions. 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. If the constant is greater than 1, we get a vertical stretch; if the constant is between 0 and 1, we get a vertical compression.
