Functions Defined by Tables
Functions defined by tables is a Grade 7 math skill from Yoshiwara Intermediate Algebra where students interpret a table of input-output pairs as a function. Each input must map to exactly one output, and students use the table to evaluate the function, identify domain and range, and check the function property.
Key Concepts
Property When we use a table to describe a function, the first variable in the table (the left column or top row) is the input variable, and the second variable is the output. We say that the output variable is a function of the input. A table does not represent a function if a single input value corresponds to more than one output value.
Examples A table shows hours worked ($h$) and earnings ($E$). If for every value of $h$ there is only one value for $E$, then $E$ is a function of $h$. For example, if $h=5$ always results in $E=75$ dollars.
This table defines $y$ as a function of $x$ because each $x$ value has exactly one corresponding $y$ value: $|x: 1, 2, 3|, |y: 5, 10, 15|$.
Common Questions
How is a function represented by a table?
A table shows a list of input (x) values and their corresponding output (y) values. If every x-value maps to exactly one y-value, the table defines a function.
How do you determine if a table represents a function?
Check that no input value appears twice with different outputs. If any x repeats with different y-values, it is not a function.
How do you find f(3) from a table?
Look up the row where x = 3 and read the corresponding y-value. That is f(3).
What are the domain and range of a function from a table?
The domain is the set of all x-values listed, and the range is the set of all corresponding y-values.