Function or Not a Function

Front

What is a function?

Back

A function is a relation where each input (x-value) has exactly one output (y-value).

Front

What is the definition of domain in a function?

Back

The domain is the set of all possible input values (x-values) for a function.

Front

What is the definition of range in a function?

Back

The range is the set of all possible output values (y-values) for a function.

Front

What does it mean if a relation is not a function?

Back

A relation is not a function if at least one input (x-value) is associated with more than one output (y-value).

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function; if a vertical line intersects the graph at more than one point, it is not a function.

Front

What is the horizontal line test?

Back

The horizontal line test checks if a function is one-to-one; if a horizontal line intersects the graph more than once, the function is not one-to-one.

Front

Given the relation {(1,2), (2,3), (1,4)}, is it a function? Why?

Back

No, because the input 1 is associated with two different outputs (2 and 4).

Front

Identify the domain and range of the function {(3,5), (4,6), (5,5)}.

Back

Domain: {3, 4, 5}; Range: {5, 6}.

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output (y-value) is associated with exactly one input (x-value).

Front

What is the relationship between functions and relations?

Back

All functions are relations, but not all relations are functions.