### Home > APCALC > Chapter 1 > Lesson 1.2.1 > Problem1-27

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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