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give a example of the graph that has two vertical asymptotes of x=2 and x=7
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Any function of x that contains 1/(x-2) and 1/(x-7) has asymptotes at x=2 and x=7 because each expression produces division by zero, which creates an infinite gradient, and an infinite gradient is a line perpendicular to the x-axis. f(x)=1/(x-2)-1/(x-7), f(x)=1/(x-2)+1/(x-7) are examples. Another example is f(x)=1/(x²-9x+14).

The graphs are respectively shown in blue, red and green.

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