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Understanding function notation is key to working with various mathematical functions. In the context of our SAT Math practice problem, we are using function notation with the example function given as \(f(x) = x^2 - ax\).

Function notation is a way to name a function that is to be evaluated at a particular value, which is denoted by the argument in parentheses beside the function symbol. For example, \(f(x)\) denotes a function named 'f' evaluated with the variable 'x'. When you see \(f(a)\), it indicates that we are using the value 'a' in place of every instance of 'x' in our function.

This notation helps in distinguishing between the function itself and the function's value at a particular point. It is especially useful for evaluating functions at specific points, which you often need to do in algebra and calculus.

An algebraic expression is a mathematical phrase that can contain ordinary numbers, variables (like \(x\) or \(a\)), and operations such as addition and multiplication. In our SAT example, \(f(x) = x^2 - ax\) is an algebraic expression made up of variables, exponents, and an arithmetic operation—subtraction in this case.

To evaluate algebraic expressions, we replace the variables with numbers and complete the required operations. This process is fundamental when you’re trying to solve various algebra problems, as it provides a method to represent problems in a structured way.

In learning how to manipulate algebraic expressions effectively, students develop a greater understanding of mathematical concepts and how they can be applied in different types of calculations.

Simplifying equations is the process of condensing an expression into its most efficient form. This makes complex equations more manageable and easier to understand. In our SAT question, after substituting \(a\) in for \(x\), we get \(f(a) = a^2 - aa\).

To simplify this expression, we recognize that \(a^2 - aa\) equals \(a * a - a * a\), and when the same number is subtracted from itself, the result is zero.

Simplification covers combining like terms, reducing fractions, and applying exponent rules, among other techniques. Students need to be familiar with these rules to simplify equations correctly and efficiently, which is a skill frequently tested in SAT Math problems.