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For the graph the rational function #y=(x-1)/(x-2)#, which quadrants does the graph pass?

Answer 1

Eli Assouline

The quadrants are 1, 2, and 4.

This is the function's graph:

graph{y=(x-1)/(x-2) [-10, 10, 5, 5, 10]}

Given: #y=(x-1)/(x-2)#

There are 4 regions for x, #x<0, 0< x <1, 1 2#

When #x < 0, y > 0# and this is the 2nd quadrant.

When #0 0# and this is the 1st quadrant.

When #,1 < x < 2, y < 0# and this is the 4th quadrant.

When #x > 2, y > 0# and this is the 1st quadrant.

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Answer 2

Genesis Allen

The graph of the rational function y = (x - 1)/(x - 2) passes through Quadrants I and III.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.