4.1.3 Writing Function Rules Key Objectives • Write equations from function tables.
• Evaluate functions using function notation. • Identify independent and dependent variables. • Write functions. • Identify reasonable domain values and find corresponding range values. Key Terms • A function is a rule that relates two quantities so that each input value corresponds exactly to one output value. • A function rule is an algebraic expression that defines a function. • Function notation is the notation used to describe a function. • An independent variable is the input of a function; a variable whose value determines the value of the output, or dependent variable. • A dependent variable is the output of a function; a variable whose value depends on the value of the input, or independent variable.
Example 1 Writing Equations from Function Tables
To write an equation for a function that corresponds to the ordered pairs in a table, first identify possible relationships between the x - and y -values in the first ordered pair. In the table in Example 1, the x - and y -values in the first ordered pair are 2 and 12. Possible relationships between these values include • multiply x by 6 to get y • multiply x by 2 and add 8 to get y • multiply x by 3 and add 6 to get y • multiply x by 4 and add 4 to get y • multiply x by 5 and add 2 to get y Then, determine which of those relationships (if any) works for the remaining ordered pairs in the table. Once the correct relationship has been identified, translate that relationship to an equation.
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