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The substitution method is a fundamental technique in algebra that involves replacing variables with their corresponding values or expressions. This method is particularly useful when you want to evaluate a function at different points. When you substitute a value into the function, you effectively see what the function outputs for that specific input.

For instance, in the exercise \(g(x) = 2x - 3\), to find \(g(-x)\), you substitute \(x\) with \(\-x\). Think of it as giving the function a new input and observing the output. Here, rather than asking what \(2 \times x\) minus three is, you're asking what \(2 \times (-x)\) minus three equals. It changes the function's behavior slightly—an important observation when dealing with negative numbers. The substitution method is a straightforward yet powerful tool in algebra that helps you understand and visualize the behavior of functions for different inputs.

Linear functions are the simplest form of functions where the relationship between the input (often \(x\)) and the output is a straight line when plotted on a graph. These functions follow the general form \(f(x) = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. The slope indicates the steepness of the line, while the y-intercept tells you where the line crosses the y-axis.

The exercise's given function \(g(x) = 2x - 3\) is a linear function. Its slope is 2, which means for every one-unit increase in \(x\), \(g(x)\) increases by 2 units. The y-intercept is -3, which means the line will cross the y-axis at the point (0, -3). Understanding these components is crucial because they define the rate of change and starting value for any linear relationship.

Algebraic expressions are combinations of numbers, variables, and arithmetic operations like addition, subtraction, multiplication, and division. They represent values that can change, based on the variables involved. Unlike equations, expressions do not have an equal sign; they are not claiming to be equal to anything.

In the context of the provided exercise, the expression \(2x - 3\) is an algebraic expression. It communicates a relationship between the variable \(x\) and numbers 2 and -3, indicating that you should multiply \(x\) by 2 and then subtract 3 from the result. When evaluating expressions such as \(g(a+h)\), which involve more than one variable or terms added to a variable, it's important to apply the distributive property correctly. For example, \(g(a+h) = 2(a+h) - 3\) involves distributing the 2 to both \(a\) and \(h\) before subtracting 3. Grasping the concept of algebraic expressions is key in solving a wide range of problems in algebra.