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course MTH 163
Oct. 20, 2012 @ 1:21 PM
Make tables and sketch graphs of y = x, y = x 2 , y = x -1 and y = 2 x , for x = -3 to x = 3. Show what happens to each graph if it is vertically stretched by factor 2.
For each graph, the actual form doesn’t change, but the actual shapes either shrink or change angle. For example, with y = x and y = 2x, the linear graph increases in slope.
For the quadratic graph, y = x^2, the parabola will become more narrow when stretched by a factor of two.
For the power function, the graphs will become exceedingly farther away from the corner of quadrants II and III.
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Good answers.
Note that you should be thinking in terms of the effect on basic points.
The basic points of a power function are in general the points where x = -1, 0, 1/2, 1 and 2. If you understand what happens at those points, you have a very good basis for understanding the overall behavior of the graph.
For example, x^(-1) takes values -1, 2, 1 and 1/2 and x = -1, 1/2, 1 and 2, and is undefined at x = 0. As x approaches zero x^(-1) the magnitude of x becomes larger and larger without bound forming the vertical asymptote. ... etc ..
The factor 2 moves each of the basic points twice as far from the x axis, as you understand.
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