Understanding functions

Front

What is a function?

Back

A function is a set of ordered pairs where each input (x value) is associated with exactly one output (y value).

Front

Which of the following is a function? {(1,2), (2,3), (3,4), (1,5)}

Back

Not a function, because the input '1' is associated with two different outputs (2 and 5).

Front

What does it mean for a relation to be a function?

Back

A relation is a function if every input has exactly one output.

Front

Identify the ordered pair that can be added to the set {(0,1), (1,4), (2,3), (3,2), (4,8)} to keep it a function: (0,5), (1,6), (4,-5), (5,4)

Back

(5,4) can be added because it does not repeat any x value.

Front

Which set of ordered pairs 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 all x values are unique.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a relation is a function. If a vertical line intersects the graph 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 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

True or False: A function can have the same y value for different x values.

Back

True, a function can have the same y value for different x values as long as each x value is unique.