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2 answers:
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Answer:
Vertical asymptote:
Horizontal asymptote:
Domain of f(x) is all real numbers except 3.
Range of f(x) is all real numbers except 2.
Step-by-step explanation:
Given:
Function:
One root,
To find:
Vertical and horizontal asymptote, domain, range and roots of f(x).
Solution:
First of all, let us find the roots of f(x).
<em>Roots of f(x) means the value of x where f(x) = 0</em>
One root,
Domain of f(x) i.e. the values that we give as input to the function and there is a value of f(x) defined for it.
For x = 3, the value of f(x)
For all, other values of ,
is defined.
Hence, Domain of f(x) is all real numbers except 3.
Range of f(x) i.e. the values that are possible output of the function.
f(x) = 2 is not possible in this case because something is subtracted from 2. That something is .
Hence, Range of f(x) is all real numbers except 2.
Vertical Asymptote is the value of x, where value of f(x) .
It is possible only when
vertical asymptote:
Horizontal Asymptote is the value of f(x) , where value of x .
Horizontal asymptote:
Please refer to the graph of given function as shown in the attached image.
