y

x

y

x

Let’s start off by graphing the simplest hyperbola:

X Y

Graph the rational functions. Find the Horizontal and Vertical Asymptotes. Then find the domain and range of the function, and the x and y-intercepts.

The first form of hyperbolic graphs is , with vertical asymptote x = h, and

horizontal asymptote y = k. Make sure to draw both branches of the hyperbola.

1)

HA: ________________________

VA: ________________________

Domain: _____________________

Range: ______________________

X- Int: _______________________

Y- Int: _______________________

y

x

y

x

2)

3)

HA: ________________________

VA: ________________________

Domain: _____________________

Range: ______________________

X- Int: _______________________

Y- Int: _______________________

HA: ________________________

VA: ________________________

Domain: _____________________

Range: ______________________

X- Int: _______________________

Y- Int: _______________________

y

x

y

x

The second form of hyperbolic graphs is of the form , with vertical

asymptote at the x-value that makes the denominator zero, and horizontal asymptote at

.

4)

5)

HA: ________________________

VA: ________________________

Domain: _____________________

Range: ______________________

X- Int: _______________________

Y- Int: _______________________

HA: ________________________

VA: ________________________

Domain: _____________________

Range: ______________________

X- Int: _______________________

Y- Int: _______________________