In this section of the SAT, strange looking questions may confuse those taking the exam without a little bit of knowledge about these types of questions - particularly functions. Some function questions are common while other ones - more difficult - are thankfully rare.
Functions
Functions can be graphed as a line in some cases, but for algebra a function is just an equation. So, 3y = 2x + 5 would be a function. Functions are different than regular equations in that they will be written as f(x) or h(x). The f(x) will replace the y value after the equation is solved for y originally.
A function is merely a series of steps to perform. The big difference comes in how these questions are written on the SAT math section. While normal equations may be written out, functions (like f(x) for example) will be written slightly different which can be confusing for some people taking the SAT.
Domain and Range
The domain of a function refers to what is put into the equation to get the answer. It is the possible X values for the equation. On the other hand, range refers to what is got out of the equation. If the question asks for the domain they want to know "what values of X are definitely possible."
Let's talk about domain and range. The domain of a function is what you put into the equation in order to get an answer. Basically, it means the possible x values. Range is what you get out of the equation, or, your y or f(x) values. So if they're asking for the domain of the question, they're asking "what values of x are possible in this equation?"
TIP: Sometimes values can affect domain or range, which can have an effect on the final answer. Absolute values and square roots both are only positive and a zero cannot appear in a denominator.
BONUS TIP: It is a good idea to try 0, 1, negatives and fractions in these types of problems because this can test the limits of range.
Occasionally a specific domain for the function will not be given. In these cases, it is a good idea to focus on finding the minimum value of the function.
