Domain and Range 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

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

Back

No, because the input 1 has two different outputs (2 and 4).

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

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

Back

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

Front

Identify the domain of the relation {(0,1), (1,-3), (2,-4), (-4,1)}.

Back

The domain is {-4, 0, 1, 2}.

Front

Identify the range of the relation {(0,1), (1,-3), (2,-4), (-4,1)}.

Back

The range is {-4, -3, 1}.

Front

What does it mean if a function is not defined for a certain x-value?

Back

It means that there is no corresponding y-value for that x-value in the function.

Front

For the function f(x) = x^2, what is the range?

Back

The range is all non-negative real numbers [0, ∞).

Front

What is the vertical line test?

Back

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.