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A linear function is a type of function where the relationship between variables is represented by a straight line when plotted on a graph.
For instance, the function given in the exercise is a linear function: \(g(x) = 2x + 3\).
The general form of a linear function is \(f(x) = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
Simple properties of linear functions include:

• Constant rate of change
• Graph is a straight line
• No bends or curves

Linear functions are foundational in understanding more complex relationships in algebra.

The domain of a function represents all the possible input values (x-values) that the function can accept.
For different types of functions, domain constraints can vary.
For example, the domain of the square root function \(f(x) = \sqrt{x}\) is limited to non-negative numbers because the square root of a negative number is not a real number.
However, linear functions like \(g(x) = 2x + 3\) do not have such constraints.
Since there are no fractions or square roots involved, linear functions can accept any real number as input.
This results in an unrestricted or infinite domain.
When identifying domain constraints, always check for operations that include squares, roots, or divisions by variables.

In mathematics, real numbers include all the numbers that can be found on the number line.
This includes all the integers, fractions, and irrational numbers.
Simply put, real numbers are everything except imaginary numbers.

• Positive and negative integers: -3, -2, -1, 0, 1, 2, 3
• Fractions and decimals: 1/2, 0.75
• Irrational numbers: \pi, e\

Functions like \(g(x) = 2x + 3\) that have a domain of all real numbers can take any of these values as inputs.
Real numbers are fundamental in everyday calculations and higher mathematics, offering a versatile and comprehensive set of values for various applications.