Jump to a New ChapterIntroductionThe Discipline of DisciplineSAT StrategiesThe SAT Personal TrainerMeet the Writing SectionBeat the EssayBeat Improving SentencesBeat Identifying Sentence ErrorsBeat Improving ParagraphsMeet the Critical Reading sectionBeat Sentence CompletionsReading Passages: The Long and Short of ItThe Long of ItThe Short of ItSAT VocabularyMeet the Math SectionBeat Multiple-Choice and Grid-InsNumbers and OperationsAlgebraGeometryData, Statistics, and Probability
 19.1 To Algebra or Not to Algebra? 19.2 A Very Short Algebra Glossary 19.3 Substitution Questions 19.4 Solving Equations 19.5 Algebra, ABSOLUTE Value, and Exponents 19.6 Beat the System (of Equations) 19.7 Inequalities 19.8 Binomials and Quadratic Equations

 19.9 Variation 19.10 How Do Functions Function? 19.11 Evaluating Functions 19.12 Compound Functions 19.13 Domain and Range 19.14 Functions As Models 19.15 Defeating Word Problems 19.16 The Most Common Word Problems
How Do Functions Function?
Functions are one of the most important additions to the Math section of the new SAT. So, what’s a function? A function describes a relationship between one or more inputs and one output. The inputs to a function are variables such as x; the output of the function for a particular value of x is usually represented as f(x) or g(x). In the function f(x) = 2x, the output of the function is always equal to two times the value of x. So, if x = 1, then f(x) = 2, and if x = 12, then f(x) = 24.
So far, it may seem as if a function is just another word for equation. Based on the way the SAT generally tests functions, it’s fine to think of functions that way. However, all functions follow a special rule that you’ve got to know:
For every input x, a function can have only one value for f(x).
You might be asking yourself what this math babble means. Here’s an example that should help translate. Take the equation |y| = x. Because y sits between absolute value brackets, if x = 2, then y could be equal to either 2 or –2. This equation can’t be a function, because for each value of x, there are two possible values of y.
 Jump to a New ChapterIntroductionThe Discipline of DisciplineSAT StrategiesThe SAT Personal TrainerMeet the Writing SectionBeat the EssayBeat Improving SentencesBeat Identifying Sentence ErrorsBeat Improving ParagraphsMeet the Critical Reading sectionBeat Sentence CompletionsReading Passages: The Long and Short of ItThe Long of ItThe Short of ItSAT VocabularyMeet the Math SectionBeat Multiple-Choice and Grid-InsNumbers and OperationsAlgebraGeometryData, Statistics, and Probability
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