Question

Find the domain and range of the function. $$f(x)=3 x$$

   Find the domain and range of the function.
$$f(x)=3 x$$

College Algebra

College Algebra

James Stewart,… 7th Edition

Chapter 2, Problem 51

Instant Answer

Solved by Expert Carson Merrill

07/07/2021

Step 1

The given function is \( f(x) = 3x \), which is a linear function. Linear functions are of the form \( f(x) = ax + b \), where \( a \) and \( b \) are constants. In this case, \( a = 3 \) and \( b = 0 \). Show more…

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Find the domain and range of the function. $$f(x)=3 x$$

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Key Concepts

Range

The range of a function is the set of all possible output values that the function can produce. For functions that are linear and have a constant nonzero multiplier, the range is typically all real numbers, as outputs can cover every real value.

Function

A function is a mathematical relation that assigns exactly one output value for each input value in its domain. Understanding functions involves knowing how inputs (domain) relate to outputs (range) based on the established rule or formula.

Domain

The domain of a function is the complete set of possible input values for which the function is defined. In many cases, such as with linear functions, the domain is all real numbers since there are no restrictions on the inputs.

Linear Function

A linear function is a function whose graph forms a straight line, typically represented as f(x) = mx + b, where m and b are constants. This type of function is characterized by its constant rate of change, and both its domain and range are usually all real numbers when no additional restrictions are imposed.

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