What do you think our domain is?
What about our range?
What do you think our domain is?
What about our range?
There are two ways to write a rational function
There are two ways to write a rational function: Way One
Our asymptote at x = h is because it is outside of our domain, X DOES NOT EXIST THERE, so our graph cannot exist there.
Our asymptote at y = k is because it is outside of our domain, Y DOES NOT EXIST THERE, so our graph cannot exist there.
There are two ways to write a rational function: Way Two
Our vertical asymptote is where x cannot exist. So where cx+d (the denominator) is equal to zero. It is NOT in the domain.
Our horizontal asymptote is where y does not exist, meaning y = a/c is not in the range.
Graphing Rational FunctionsStep 1: find and draw the vertical and horizontal asymptotes
Step 2: create a table with two x values to the left of the vertical asymptote, and two x values to the right of the vertical asymptote
Step 3: complete the table for the y values and graph the four points
Step 4: draw a hyperbola through the points and avoid crossing any asymptotes