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1-27.

Sketch the graph of y = $\frac { 1 } { x }$. 1-27 HW eTool (Desmos). Homework Help ✎

1. Why does this graph have a vertical asymptote? What is the equation of that asymptote?

Vertical asymptotes are lines with undefined slopes. Their equations are of the form: x = k where k is a constant.

2. State the equation of the horizontal asymptote.

Consider the horizontal lines that you found in problem 1-22(b).

Horizontal asymptotes are lines with 0 slope. Their equations are of the form: y = 0x+b or y = k, where k is some constant.

3. Alter the equation y = $\frac { 1 } { x }$ so that the vertical asymptote is x = 1 and the horizontal asymptote is y = 3.

$y=\frac{1}{x-h}+k$

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