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), (2,3), (3,4)} a function?

Back

Yes, because each x-value has only one y-value paired with it.

Front

Is the relation {(1,2), (1,3), (2,4)} a function?

Back

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

Front

What is the domain of the function {(0,1), (1,-3), (2,-4), (-4,1)}?

Back

D: {0, 1, 2, -4}.

Front

What is the range of the function {(0,1), (1,-3), (2,-4), (-4,1)}?

Back

R: {1, -3, -4}.

Front

How can you determine if a graph represents a function?

Back

Use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

Front

What is the vertical line test?

Back

A method to determine if a graph is a function by checking if a vertical line crosses the graph more than once.

Front

What is an example of a function?

Back

f(x) = 2x + 3 is a function because for every x, there is one corresponding y.

Front

What is a non-function example?

Back

y^2 = x is not a function because for some x-values, there are two corresponding y-values.

Front

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

Back

A one-to-one function means that each output is paired with exactly one input, and no two inputs share the same output.