Hyperbolas and Circles

Learning Targets

To recognize and describe the characteristics of a hyperbola and circle.

To relate the transformations, reflections and translations of a hyperbola and circle to an equation or graph

Hyperbola

A hyperbola is also known as a rational function and is expressed as INSERT EQUATION

GRAPH

Hyperbola Characteristics

Graph

The characteristics of a hyperbola are:• Has no vertical or

horizontal symmetry• There are both horizontal

and vertical asymptotes• The domain and range is

limited

Locator Point

Graph

The locator point for this function is where the horizontal and vertical asymptotes intersect.

Therefore we use the origin, (0,0).

Standard Form

Impacts of h and k

Graph

Based on the graph at the right what inputs/outputs can our function never have?

This point is known as the hyperbolas ‘hole’

Impacts of h and k

Graph

The coordinates of this hole are actually the values we cannot have in our domain and range.

Domain: all real numbers for x other than h

Range: all real numbers for y other than k

Impacts of h and k

Graph

This also means that our asymptotes can be identified as:

Vertical Asymptote: x=h

Horizontal Asymptote: y=k

Example #1

Example #2

Impacts of a

Graph

Our stretch/compression factor will once again change the shape of our function.

The multiple of the factor will will determine how close our graph is to the ‘hole’

The larger the a value, the further away our graph will be.

The smaller the a value , the closer our graph will be.

Example #3

Graph

Circle