Quick Answer
A function is a mathematical relationship where each input maps to exactly one output. On the Digital SAT, functions are tested heavily in the Math section, appearing in approximately 25% of Algebra and Advanced Math questions. Students must evaluate equations or interpret graphs to identify specific output values.
A function is a relation that assigns each element in the domain to exactly one element in the range, typically denoted by the notation f(x) = y. In this context, x represents the independent variable (input) and f(x) represents the dependent variable (output).
Question: If f(x) = 2x^2 - 3x + 7, what is the value of f(3)? Solution: Substitute 3 for every instance of x in the function: f(3) = 2(3)^2 - 3(3) + 7. f(3) = 2(9) - 9 + 7. f(3) = 18 - 9 + 7 = 16. The value of f(3) is 16.
Mistake 1: Treating f(x) as 'f times x' instead of a notation representing the output value.
Mistake 2: Swapping inputs and outputs, such as plugging a given y-value into the x-variable position during evaluation.
Mistake 3: Failing the vertical line test by assuming any curved line on a graph represents a function even if one x-value has multiple y-values.
Students targeting 750+ should know that the SAT often tests 'nested' or composite functions, such as f(g(x)). To solve these efficiently, always work from the inside out: evaluate the inner function g(x) first to find a numerical value, then use that result as the input for the outer function f.
Domain (Function)
Domain (Function) represents the set of all possible input values for which a function is defined. On the Digital SAT, domain questions typically appear in the Math section, specifically within the Algebra or Advanced Math modules. These questions frequently involve interpreting graphs or rational expressions and occur approximately 1-3 times per test.
Linear Equation
A linear equation is an algebraic statement where the highest power of the variable is one. On the Digital SAT, these equations appear frequently in Math Modules 1 and 2, typically accounting for approximately 30% of the Algebra domain. Mastering them is essential for solving word problems and interpreting graphs.
Function Notation
Function notation is a mathematical shorthand, using symbols like f(x), to define relationships between inputs and outputs. On the Digital SAT, this concept appears frequently in the Heart of Algebra section, typically appearing in approximately 10-15% of math questions. It requires students to evaluate expressions or interpret graphical data through functional relationships.
Input and Output
Input and output describe the relationship between independent and dependent variables within a function. On the Digital SAT, these concepts are tested frequently in the Algebra and Advanced Math modules. Typically, students will encounter approximately 4 to 6 questions per exam that require evaluating functions or interpreting graph coordinates.
A function on the SAT is a rule where every input value corresponds to exactly one output value. This concept is central to the Math section of the Digital SAT, appearing across various question types including linear equations and quadratic models. Typically, functions are presented using f(x) notation, and students must be able to solve for values using equations, tables, or graphs.
To evaluate a function, you take the provided input value and substitute it for every instance of the independent variable, usually x, within the function's expression. After substitution, you simplify the expression using the standard order of operations (PEMDAS). For example, to find f(2) for the function f(x) = 5x + 1, you calculate 5(2) + 1 to get an output of 11.
The difference between a function and a relation is that a function is a specific type of relation where each input has exactly one output. While all functions are relations, not all relations are functions. On the SAT, you can identify a function on a graph if it passes the Vertical Line Test, meaning no vertical line touches the graph at more than one point.
You will typically encounter approximately 10 to 15 questions that involve functions or function notation across the two Math modules of the Digital SAT. These questions appear in various formats, such as identifying intercepts, calculating growth in exponential models, or shifting graphs. Because they span across Algebra and Advanced Math, they are essential for achieving a high score.
