Functions, Functions, Functions

Front

What is a function?

Back

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

Front

Is the relation {(1,2), (1,3)} a function? Why?

Back

No, because the x-value 1 has two different y-values (2 and 3).

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

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

Front

Identify if the following is a function: {(2,3), (3,4), (2,5)}

Back

Not a function, because the x-value 2 has two different y-values (3 and 5).

Front

What does it mean for a function to be one-to-one?

Back

A one-to-one function means that each output (y-value) is paired with exactly one input (x-value).

Front

Given the function f(x) = 2x + 3, what is f(2)?

Back

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

Front

What is a vertical line test?

Back

A method to determine if a relation is a function by checking if any vertical line intersects the graph at more than one point.

Front

If f(x) = x^2, what is the output for f(-3)?

Back

f(-3) = (-3)^2 = 9.

Front

What is the difference between a function and a relation?

Back

A relation can have multiple outputs for a single input, while a function cannot.