Understanding functions

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

How can you determine if a table represents a function?

Back

A table represents a function if there are no repeating x-values (inputs).

Front

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

Back

A relation is not a function if at least one input is related to more than one output.

Front

Given the set of ordered pairs {(1,2), (2,3), (3,4)}, is this a function?

Back

Yes, because each input (x-value) is unique.

Front

Given the set of ordered pairs {(1,2), (1,3), (2,4)}, is this a function?

Back

No, because the input '1' is related to two different outputs (2 and 3).

Front

What is the vertical line test?

Back

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

Front

If f(x) = 2x + 3, what is f(2)?

Back

f(2) = 2(2) + 3 = 7.

Front

What is the domain of a function?

Back

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

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

Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, as long as each input corresponds to only one output.