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course Mth 163
1-24-13 1:19
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.
All of these are stretched in the y- direction.
Y=x is a line with a slope of 1. If you stretched it vertically by 2 the slope will be 2.
Y=x^2 is a parabola with a vertex at (0,0). If it is stretched it will get skinnier with major points at (1,2) and (-1,2).
Y=x^-1 is a hyperbola with a vertical asymptote at 0. If it is stretched by 2 then the major point is at (-1,-2) and at (1,2).
Y=2^x is an exponential function with a horizontal asymptote at 0. If it is stretched by 2 then there will still by a horizontal asymptote at 0, but it would cross the y axis is at 2 instead of 1.
X=-3 is a constant function with a horizontal line running through -3. If it is stretched by 2 it would stay the same.
X=3 is a constant function with a horizontal line running through 3. If it is stretched by 2 it would stay the same.
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x = -3 and x = 3 are vertical, not horizontal lines. If they were horizontal then vertical stretching would affect them.
However the phrase 'for x = -3 to x = 3' indicates simply that the domain over which we consider these functions, for this particular question, is the interval [-3, 3].
In any case, very well done.
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