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Good day students in this clip is very going over some examples that have the review how to generate graphs of rational functions so let us take a look at question number one we are to determine the equation of any vertical asymptotes and the values of X for any holes in the graph okay so how do you find the holes and vertical asymptotes within a start out by origin of the procedures for finding each so to find the holes of you set factors that counsel out to the cancel out to zero and then sold so you have a rational function the fact that the numerator the denominator any factor that's common in the numerator and denominator that he can cancel out our are your of real are are the equations that she used to solve for the holes okay for right so of let's talk about the vertical asymptotes how the find the vertical asymptote to find a vertical asymptote is an is set of fact or is coming denominator factors set denominator factors set denominator or factors. That do not cancel out cannot cancel out said those one's equal to zero and solve okay so the weather cancel out tell your polls your holes in the one that the accounts will tell your vertical asymptotes him just for your information holes are also known as your of removable discontinuities right and vertical asymptotes also known as your polls or infinite discontinuities in right so let's go ahead and find the holes first so to determine what the holes are we have to determine what factors cancel out okay so what on the numerator the denominator now what does the numerator the denominator have in common in order to answer that we have to factor out the denominator okay so let's use the AC method here of AC is tan and D is negative seven two numbers that work your negative five and negative to we do not need to factor by grouping here because a is one right so this is equal to X minus five divided by X minus five times X minus two nine examine this function what do you notice he notice that X minus five Is common in the numerator the denominator so you can be cancel out the constant goes here one express that goes here one switchable factor cancels out that tells you the holes right so to find the holes the steps the factor that cancel out equal to zero and solve the add five to both sides the have X equals five there goes the hole in a to find your vertical asymptotes vertical asymptotes all you do is you look at the denominator and extract factors that did not Get cancel out okay the reduced form of polynomial expression you set the denominator of of that's polynomial to zero so in this case X minus two dozen have any, factor numerator so we just extracted set equal to zero and solve X equals to is our vertical asymptotes alright so, see where the answer holes find out is it's a cannot be here be vertical asymptote of two side answer is option letter c right let's take a look at question number two we have a transformed of rational function here F
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