Test 3 Functions and Relations

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. In other words, for every x in the domain, there is one and only one y in the range.

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

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

Front

How can you determine if a graph represents a function?

Back

A graph represents a function if any vertical line drawn through the graph intersects it at most once (Vertical Line Test).

Front

What does it mean for a relation to not be 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 notation for a function?

Back

The notation for a function is typically written as f(x), where f is the function name and x is the input variable.

Front

What is f(5) if f(x) = -2x + 3?

Back

f(5) = -2(5) + 3 = -10 + 3 = -7.

Front

What is the difference between a relation and a function?

Back

A relation is any set of ordered pairs, while a function is a specific type of relation where each input is associated with exactly one output.

Front

What is a table of values in relation to functions?

Back

A table of values lists pairs of input (x) and output (y) values that correspond to a function, helping to visualize the relationship.

Front

What does it mean for a function to be linear?

Back

A linear function is a function that graphs to a straight line, typically represented in the form f(x) = mx + b, where m is the slope and b is the y-intercept.