Understanding asymptotes can really help you get a better handle on rational functions.
Asymptotes show how a function behaves as it gets close to certain values, especially as it goes to infinity or hits undefined points.
Vertical Asymptotes: These are spots where the function can't be defined, usually where the denominator is zero. For example, in the function ( f(x) = \frac{1}{x-2} ), there is a vertical asymptote at ( x=2 ).
Horizontal Asymptotes: These show how a function behaves as ( x ) goes towards infinity. For example, in ( g(x) = \frac{2x+3}{x+1} ), as ( x ) gets really big, the horizontal asymptote is ( y=2 ).
Oblique Asymptotes: These can be found in some rational functions. They happen when the degree (or highest power) of the numerator is one more than that of the denominator.
By spotting these asymptotes, you can draw more accurate graphs and predict how the function behaves. This makes working with rational functions much easier!
Understanding asymptotes can really help you get a better handle on rational functions.
Asymptotes show how a function behaves as it gets close to certain values, especially as it goes to infinity or hits undefined points.
Vertical Asymptotes: These are spots where the function can't be defined, usually where the denominator is zero. For example, in the function ( f(x) = \frac{1}{x-2} ), there is a vertical asymptote at ( x=2 ).
Horizontal Asymptotes: These show how a function behaves as ( x ) goes towards infinity. For example, in ( g(x) = \frac{2x+3}{x+1} ), as ( x ) gets really big, the horizontal asymptote is ( y=2 ).
Oblique Asymptotes: These can be found in some rational functions. They happen when the degree (or highest power) of the numerator is one more than that of the denominator.
By spotting these asymptotes, you can draw more accurate graphs and predict how the function behaves. This makes working with rational functions much easier!