Functions, Functions, Functions!

Front

What is a function?

Back

A function is a relation where every input has only ONE output.

Front

What does the vertical line test determine?

Back

The vertical line test determines 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 domain of a function?

Back

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

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

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

Back

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

Front

What is an example of a function?

Back

An example of a function is f(x) = x^2, where each x-value has a unique y-value.

Front

What is a relation?

Back

A relation is a set of ordered pairs, which may or may not be a function.

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 has only one output.

Front

What is an example of a non-function?

Back

An example of a non-function is the relation {(1, 2), (1, 3)}, where the input 1 has two different outputs.

Front

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

Back

A function is one-to-one if it never assigns the same value to two different domain elements.