10 Consider the following Use a graphing utility to graph th

10. Consider the following:

Use a graphing utility to graph the function.

Determine the domain of f.

all real numbers

all real numbers except 3    

all real numbers except -3

all real numbers except 9

all real numbers except -9

all real numbers except 3 and 9

all real numbers except -3 and -9

Identify any vertical asymptotes of f. (If there are no asymptotes, enter NONE.)
x =

Identify any horizontal asymptotes of f. (If there are no asymptotes, enter NONE.)
f(x) =

Solution

-x / (x - 3)^2

domain :
Clearly x cannot be 3 else, denominator becomes ZERO

So, domain is :
all real numbers except 3
Option 2

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Vertical asymptotes :
x = 3

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Horiz asymptotes :
Degree of numerator = 1 as it is linear
Degree of denominator =2 as it is quadratic

Since the deg of numerator LESS THAN deg of denominator,
the horizontal asymptote is :

f(x) or y = 0