What are the domain, range, and asymptote of h(x) = 6x – 4? domain: {x | x is a real number}; range: {y | y > 4}; asymptote:
2 answers:
Answer:
Step-by-step explanation:
The domain of a function is the set for which the function is defined. Our function is the function . This function is defined regardless of the value of x, so it is defined for every real value of x. That is, it's domain is the set {x|x is a real number}.
The range of the function is the set of all possible values that the function might take, that is {y|y=6x-4}. Recall that every real number y could be written of the form y=6x-4 for a particular x. So the range of the function is the set {y|y is a real number}.
Note that as x gets bigger, the value of 6x-4 gets also bigger, then it doesn't approach any particular number. Note also that as x approaches - infinity, the value of 6x-4 approaches also - infinity. In this case, we don't have any horizontal asymptote. Since the function is defined for every real number, it doesn't have any vertical asymptote. Since h is a linear function, it cannot have any oblique asymptote, then h doesn't have any asymptote.
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