Question

This is a hyperbole question... find the y and x intercept and their horizontal and vertical asymptote

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Answer 1

• x-intercept: 1/2
• y-intercept: 1
• horizontal asymptote: y=2
• vertical asymptote: x=1

Explanation:

y-intercept

To find the y-intercept, set x=0 and solve for y.

y = 1/(0 -1) +2 = -1 +2

y = 1

x-intercept

To find the x-intercept, set y=0 and solve for x.

0 = 1/(x -1) +2

0 = 1 +2(x -1) . . . . multiply by x-1

1 = 2x . . . . . . . . . add 1, simplify

1/2 = x . . . . . . . . divide by 2

horizontal asymptote

This is the value of y as x gets very large. When that happens, the fraction with x in the denominator approaches zero, so the value of y approaches 2.

The horizontal asymptote is y = 2.

vertical asymptote

This is the value of x that makes the denominator zero.

The vertical asymptote is x = 1.