Description of transformation: Equation(s) for the Horizontal asymptote(s): Y-intercept in (x, y) form:
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A plot of y = F(x) = e^x is shown in the upper left picture. It has horizontal asymptote y=0, and y-intercept = (0, 1).
In the upper right picture, I have plotted y = F(x-5). This has the same horizontal asymptote (y=0), but a different y-intercept (0, .00674). This is the same as shifting the original curve to the right by 5 units.
The lower left picture is a plot of y = F(x) - 5 = e^x - 5. The horizontal asymptote has moved down to y=-5, and the y-intercept to (0, -4). (5 has been subtracted from all of the y values in the upper left plot, shifting the curve down by 5 units.)
The lower right picture is a plot of y = -F(x) = -e^x. The entire plot is reflected about the x-axis. The horizontal asymptote remains y=0, but the y-intercept (0, -1) is now the negative of what it was originally.
answered 4 months ago
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