Question

The graph of g(x) is transformed from its parent function, f(x). Apply concepts involved in determining the key features of a rational function to determine the domain and range of the function, .
A. What is the domain of the function, g(x)?
B. What is the range of the function, g(x)?

Answer 1

A. the domain is all real mumber exept 6
x-6=0
x=6

you solve the denominator for x to find the domain.

B. the range is all real numbers exept 0.

to find the range you have to graph it.

Answer 2

Answer: Domain= {x ∈ R | x ≠ 6}

Range = {g(x) ∈ R | g(x) ≠ 0}

Step-by-step explanation:

The given rational function : $g(x)=\dfrac{1}{x-6}$

• The domain of a function is the set of all input values of x in the function on which the function is defined.
• The range of a function is the set of all output values .

Since the given function is a rational function, so it is not defined for denominator equals to zero.

The excluded value for function : $x-6=0\Rightarrow\ x=6$

Thus, the function is defined for all real numbers except at x=6.

i.e. Domain= {x ∈ R | x ≠ 6}

Since the range of the function contains all the out put values except 0.

i.e. Range =  {g(x) ∈ R | g(x) ≠ 0}