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# Graphs of rational functions (old example)

Sal matches three graphs of rational functions to three formulas of such functions by considering asymptotes and intercepts. Created by Sal Khan.

## Want to join the conversation?

• What about seeing what everything evaluates to for a given `x` where they're all obviously different? (Like `x=0` here.) Any other ways to solve it?
• I used this approach as well. Having eliminated f(x), I noticed that g(x) was -h(x), which is clear from the graphs, as well. So considering any point where they are non-0 will identify which is which.
• What other types of graphs do we use asymptotes for?
• Inverse variation, logarithmic functions, hyperbolas, and exponential functions.
• I don't understand this video. The whole as x>to infinity is confusing
• It was introduced in earlier videos. Maybe it would help is you reviewed them? (And ask questions there if you have any. And here too.)
• how do you know when the formula for the functions gives you the y asymptote or x asymptote
• The horizontal asymptote is when the numerator divided by the denominator approaches infinity while the vertical asymptote is when the denominator is set to zero.
• how do we find the zeros in the graph when we have the least common factor?
• The L.C.M of the denominator will help you to find the vertical asymptote of the curve as when the denominator takes that value of x, the y will be infinite.
(1 vote)
• How would you solve for the Slope Asymptotes?
• At Sal says that in order to have a vertical asymptote "it cannot be defined there. " What does he mean by this? What is he referring to as it? Why can "it" not be defined?
(1 vote)
• what if 2 different functions have the same asymptotes and are equal to 0 at the same x value? How would you tell which is which?

Would you just test it at a region around where the functions are equal to 0 or is there a better way?
(1 vote)
• You could simply test an x where the y values are different (See the top question).