Question

Which graph represents the function

Answer 1

Explanation:

Your graph will have a vertical asymptote at x = 1, as the denominator x - 1 cannot equal zero. Therefore, f(1) is not posssible. Then, plugging in test values for the function on the left side of the asymptote...

`f(-1) = (2(-1)-1)/(-1-1) = (3)/(2)\\f(0) = (2(0)-1)/(0-1) = 1\\f(2) = (2(2)-1)/(2-1) = 3\\f(3) = (2(3)-1)/(3-1) = (5)/(2)`

... you will find that your graph needs to include the following points:

`(-1, (3)/(2))\\(0, 1)\\(2, 3)\\(3, (5)/(2))`

So therefore, your graph must cross through the above points, and may never cross the vertical line x = 1.