Identify Functions

Front

DOES THIS GRAPH REPRESENT A FUNCTION?

Back

A graph represents a function if every input (x-value) has exactly one output (y-value). If a vertical line intersects the graph at more than one point, it is not a function.

Front

IS THE FOLLOWING A FUNCTION?

Back

To determine if a relation is a function, check if each input has a unique output. If any input corresponds to multiple outputs, it is not a function.

Front

IS THIS EQUATION A FUNCTION? (CLUE: PLUG IN 2 FOR X AND SEE IF YOU GET THE SAME ANSWER EACH TIME)

Back

An equation is a function if substituting the same x-value always yields the same y-value. If different x-values yield the same y-value, it may still be a function.

Front

DOES THE TABLE REPRESENT A FUNCTION?

Back

A table represents a function if each input (x-value) corresponds to exactly one output (y-value). If any x-value has multiple y-values, it is not a function.

Front

IS THE FOLLOWING NOT A FUNCTION?

Back

A relation is not a function if there exists at least one input that corresponds to multiple outputs.

Front

Definition of a Function

Back

A function is a relation that assigns exactly one output for each input.

Front

Vertical Line Test

Back

A method to determine if a graph represents a function. If a vertical line crosses the graph more than once, it is not a function.

Front

Example of a Function

Back

f(x) = 2x + 3 is a function because for every x, there is one unique y.

Front

Example of Not a Function

Back

y^2 = x is not a function because for some x-values, there are two corresponding y-values.

Front

Input and Output in Functions

Back

In a function, the input is the x-value, and the output is the y-value. Each input must have one output.