Functions

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input from a given set.

Front

How do you determine if a relation is a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value). This can be checked using the vertical line test on its graph.

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 which the function is defined.

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

Given the function f(x)=2x+1, how do you find f(2)?

Back

To find f(2), substitute 2 for x: f(2) = 2(2) + 1 = 5.

Front

What is the output of the function f(x)=2x+1 when f(x)=4?

Back

To find x when f(x)=4, set 2x + 1 = 4 and solve for x: 2x = 3, so x = 3/2.

Front

What does the notation {(0,1), (1,-3), (2,-4), (-4,1)} represent?

Back

This notation represents a set of ordered pairs, which can be used to define a function or relation.

Front

What is the significance of the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function; if any vertical line intersects the graph more than once, it is not a function.

Front

What are the x-values in the relation (9, -2), (4, 3), (8, 10), (-4, 8)?

Back

The x-values in this relation are 9, 4, 8, and -4.

Front

What are the y-values in the relation (9, -2), (4, 3), (8, 10), (-4, 8)?

Back

The y-values in this relation are -2, 3, 10, and 8.