What You Need to Know

y = k/x has vertical asymptote x = 0 and horizontal asymptote y = 0

If k > 0, branches are in quadrants 1 and 3; if k < 0, in quadrants 2 and 4

The curve never crosses either axis

Key points: substitute x = 1, 2, -1, -2 to plot branches

Key Vocabulary

A curve with two branches defined by y = k/x or xy = k

A line the curve approaches but never crosses

One of the two separate parts of a hyperbola

One of the four regions of the coordinate plane divided by the axes

Select the correct answer for each question. Click "Check Answer" to see if you are right.

Question 1

For y = 4/x, what is the value of y when x = 2?

8 6 0.5 2

Question 2

The hyperbola y = -3/x has branches in which quadrants?

Quadrants 2 and 4 Quadrants 1 and 3 Quadrants 1 and 2 All four quadrants

Question 3

Which lines are asymptotes for y = 5/x?

y = 5 and x = 5 x = 0 and y = 0 (the axes) y = x and y = -x y = 1 and x = 1