Question

Find the domain (D), range (R), and asymptote (A) of the graph of the function ƒ(x) = 5x + 6

Answer 1

The function f(x) = 5x + 6 has a domain and range of all real numbers and it does not have an asymptote.

Step-by-step explanation:

The function ƒ(x) = 5x + 6 is a linear equation, which is a polynomial of the first degree. For this kind of function, the domain (D) is all real numbers since there are no restrictions on x-values that can be plugged into the equation. Consequently, the domain is (-∞, ∞).

The range (R) is also all real numbers because as x takes on any value in its domain, the resulting y-values (or ƒ(x)) can be any real number. Therefore, the range is also (-∞, ∞).

As for the asymptote (A), linear functions do not typically have asymptotes because they do not approach a certain line without ever touching it as x approaches infinity or negative infinity. Asymptotes are often associated with rational functions or functions involving logarithms or exponents. Therefore, the function ƒ(x) = 5x + 6 does not have an asymptote.

Answer 2

f(x) = 5x+6

This is a linear equation

and its graph will be a straight line

So

Domain = (-∞,∞)

Range = (-∞,∞)

And

Asymptote = none