Representations of Functions

Front

What is a function?

Back

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

Front

Which of the following is a function? (9,5) (10,5) (9,-5) (10,-5), (3,4) (4,-3) (7,4) (3, 8), (6,-5) (7, -3) (8, -1) (9, 1), (2, -2) (5, 9) (5, -7) (1, 4)

Back

(6,-5) (7, -3) (8, -1) (9, 1) is a function because each x-value is unique.

Front

What is the vertical line test?

Back

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

Front

Is the relation {(1,2), (2,3), (1,4)} a function? Why or why not?

Back

No, because the x-value 1 has two different y-values (2 and 4).

Front

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

Back

A relation is not a function if at least one x-value is associated with more than one y-value.

Front

Is the mapping {(a, b), (a, c)} a function?

Back

No, because the x-value 'a' has two different y-values (b and c).

Front

Is the graph of y = x^2 a function?

Back

Yes, because for every x-value, there is exactly one y-value.

Front

Is the graph of y = √x a function?

Back

Yes, because for every non-negative x-value, there is exactly one non-negative y-value.

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where each x-value gives a unique y-value.

Front

What is an example of a relation that is not a function?

Back

An example is {(1, 2), (1, 3)}, where the x-value 1 has two different y-values.