Graph the function. Plot all necessary asymptotes. For vertical asymptotes, make sure there are at least two points on each side.
G(x)=x-3/x-1
To graph the function G(x) = (x-3)/(x-1), we first need to identify any asymptotes.
Horizontal asymptote:
As x approaches positive or negative infinity, the numerator and denominator will have the same degree, so we will have a horizontal asymptote at y=1.
Vertical asymptote:
The denominator cannot equal zero in order to avoid division by zero, so x=1 is a vertical asymptote for the function.
To plot the graph, we can select a few points on either side of the vertical asymptote x=1:
x=0, y=-3
x=0.5, y=-5
x=1.5, y=2
x=2, y=1
Plotting these points and connecting them with a smooth curve, we have:
Asymptotes:
Horizontal asymptote y=1
Vertical asymptote x=1
Graph:
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-5 | *
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0 1 2 3
Please note that the graph is a rough sketch and should be confirmed using a graphing tool.