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Precalculus rational function: The domain is easy but how about the range

bprp math basics

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Precalculus tutorial on finding the domain and range of a rational function without using calculus.
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11 Comments

@DarkBoo007 4 months ago

Exactly how I teach how to find the range to my Honors Pre-Calc students. Thank you for the video!

@Happy_Abe 4 months ago

The final answer is correct but might worth mentioning the y=0 case separately as then a=0 and we don’t have a quadratic and it’s not true that a degenerate quadratic is solvable when b^2-4ac≥0 if a=0, b=0, and c is not zero so if we wanted to be super precise that might be worth checking.

@jackychanmaths 4 months ago

You need to have an extra check that when y=0, x is a real number not equal to 1 or 3, and then when y=(-3-sqrt(5))/2 or y=(-3+sqrt(5))/2, the double root is not 1 or 3 as well

@PranitSuman 4 months ago

I don't know how to describe this but your videos are so interesting! If I were told to read from a book of the same concept, I probably wouldn't but watching it on YouTube makes it engaging...

@cinstruction3115 4 months ago

Great video. Answered a lot of questions for me. I went to desmos to graph it and was able to see how everything fit together. Being able to predict what the graph should look like before seeing it gives me a better understanding of the function's behavior.

@FilsdutréshautVasedhonneur 4 months ago

How are you doing ? Thanks for sharing

@Batman.Hulk.MoSiTing 4 months ago

I always found it easier to solve for the inverse of the function and then find the domain of the inverse function. Which is kinda what is happening here but it is adding extra steps to solve the first quadratic instead of just finishing the inverse function.