Algebra 1 Common Core Student Edition, Grade 8-9

Compare the graphs and asymptotes below of y = \ and y = \ + 3.

vertical asymptote at x = 0

horizontal asymptote at y = 0

vertical asymptote at x = 0

horizontal asymptote at y = 3

The graphs are identical in shape, but notice in the second graph that both the

graph and the horizontal asymptote of y = \ have been translated 3 units up.

For a rational function of the form y = ^ + c, there is a horizontal

asymptote at y = c.

Think j
How do you choose
x-values for the
table?
The vertical asymptote
is x = 1. So you should
choose x-values on either
side of 1. That way, your
sketch w ill show both
parts of the graph.

Concept Sum m ary Identifying Asymptotes

\

Words Ex a m p l e

The graph of a rational function of the form y-xl4+1

y - x _ b + c has a vertical asymptote at x — b

and a horizontal asymptote at y = c. y- x-(-4)'^1

V

vertical asymptote: x = -4

horizontal asymptote: y = 1

J

Using Vertical and Horizontal Asym ptotes

What are the asymptotes of the graph of f(x) = x f t - 2? Graph the function.

St e p 1 From the form of the function, you can see that there is a vertical

asymptote at x = 1 and a horizontal asymptote at y = —2.

St e p 2 Make a table of values

using values of x near 1.

St e p 3 Sketch the asymptotes.

Graph the function.

“5 “2-1^0234

-2.5 -3 -3.5 -5 1 -0.5 -1

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