1. ## Basic skills test

What topic in mathematics do I need to search for to be able to answer this question? Would Khan Academy have videos relevant to my needs?

$\displaystyle R(x) = \frac{x^2 - 9}{2x^2-5x-3}$

A graph of this function has which of the following sets of characteristics?

A. One vertical asymptote, one horizontal asymptote, and two equal zeros
B. Two vertical asymptotes, two horizontal asymptotes, one distinct zero, and a removable discontinuity at x = 3
C. Two vertical asymptotes, one horizontal asymptote, and two distinct zeroes.
D. One vertical asymptote, one horizontal asymptote, one distinct zero, and a removable discontinuity at x = 3

This is what I can do as of right now:

• Graph the function by plugging in a value for x and getting y.
• Set the denomintor to zero, to see what can't be on the graph

But there are some keywords I just don't understand. "Distinct zero", "Removable discontinuity", and "Equal zeros".

2. I believe a 'distinct 0' refers to one solution of $\displaystyle R(x)=0$. Two distinct 0's would then be 2 seperate solutions.
A removable discontinuity: When you put R(3) into the equation, you get $\displaystyle \frac{0}{0}$. However, when you factorise R(x), you can take out a factor of $\displaystyle (x-3)$, eliminating this undefined solution, so the discontinuity is removed.

Essentially it's just when you have factors that cancel.

Equal 0's are repeated roots.

3. Originally Posted by EMyk01
What topic in mathematics do I need to search for to be able to answer this question? Would Khan Academy have videos relevant to my needs?

$\displaystyle R(x) = \frac{x^2 - 9}{2x^2-5x-3}$

A graph of this function has which of the following sets of characteristics?

A. One vertical asymptote, one horizontal asymptote, and two equal zeros
B. Two vertical asymptotes, two horizontal asymptotes, one distinct zero, and a removable discontinuity at x = 3
C. Two vertical asymptotes, one horizontal asymptote, and two distinct zeroes.
D. One vertical asymptote, one horizontal asymptote, one distinct zero, and a removable discontinuity at x = 3

This is what I can do as of right now:

• Graph the function by plugging in a value for x and getting y.
• Set the denomintor to zero, to see what can't be on the graph

But there are some keywords I just don't understand. "Distinct zero", "Removable discontinuity", and "Equal zeros".
The topic of mathematics you are looking for is asymptotes of rational functions, as well as continuity. Both topics are often taught in calculus. Khan Academy has asymptotes here, in the algebra section, actually, but I can't see anything there on continuity.