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# Graphs of rational functions: y-intercept

Sal picks the graph that matches f(x)=(ax^m+bx+12)/(cx^m+dx+12) based on its y-intercept.

## Want to join the conversation?

• Choice C actually has a y-intercept of -2 not -1
• What is a removable discontinuity?
• It's when you have a function, and there is a "hole" in the function at a certain x-value. If you placed just 1 point on that gap, the function would be normal - hence the name removable discontinuity. For example, go to some graphing system and input y=x^3/x. The function is undefined at x=0, but with no odd behavior near it.
• What does the U shaped figure inside the Asymptotes mean? Some or U pointing up and some are U shaped pointing down.

• Those are parts of the function curves.
For example in the "A" graph, at the left-most asymptote the function changes sign and the curve jumps from −∞ to +∞.
• Rational functions can have 3 separate parabolas ?
• Technically they aren't parabolas because they have asymptotes.
• is there an easier video about asymptotes? I'm in 11th grade and have never learned this before, sad:(
• An asymptote is when the denominator equals zero. You can get this from a equation by factoring. Different from a removable discontinuity which is the other number you get when you factor but divide from the numerator as well.
• In the first line, the word 'constants', is mentioned. In the rational expression, only 12 is a constant, so why does it say the following; 'a, b, c, and d are unknown constants.'?
• Coefficients are constant values. "a, b, c and d" are the coefficients.
• In the rational expression, we have 'ax^n' and 'cx^m'. Why can't they both be ^n or ^m?
• This is likely to ensure that the 2 terms are unlike. If the exponents matched, you could add the two terms as they would be like terms.
• What's the difference between integers and unknown constants?

When it says towards the beginning; 'where m and n are integers.....'
Why couldn't it just be written as integers for both, or unknown constants for both. I don't understand why they've used integers for exponents and unknown constants for the co-efficients?
• Integers would not involve fractions or decimals. So, the exponents are being restricted to negative whole numbers, 0, or positive whole number. I think later in the video a correction box tells you to restrict the exponents to positive integers. This is likely done to keep the numerator and denominator as polynomials. Polynomials require positive exponents on the variables.

The coefficients are not being restricted - they can be any real number.