Answer:
7.) vertical asymptote: x= -3 holes: no holes (graph below, table below)
8.)vertical asymptote: x= -3 hole: (2, 1/5) (graph below, table below)
9.) vertical asymptote: none hole: (2,12) (graph below, table below)
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tep-by-step explanation:
Below are the tables/graphs
the holes/asymptotes will be solved here
7.) To solve for the vertical asymptote simplify what you can and set the denominator= 0 and solve for x
x+3=0
x= -3
8.) We can cancel out the x-2 from the numerator and denominator, set the denomiator= 0 and then solve for x
x+3=0
x= -3
Because we canceled the set of numbers there is a hole
we know that when x=2 (in the unsimplified version) the answer is undefined. To solve for the y coordinate plug in x=2 into 1/(x+3)
1/5
9.) start by factoring 3x²-12 = 3(x+2)(x-2)
same deal for the vertical asymptote (simplify what you can and set the denominator equal to 0)
cancel out the x-2 but in doing so the denominator is one and so there is no vertical asymptote
to solve for the hole plug in x=2 for 3(x+2)
get (2,12)
