functions

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) that the function can accept.

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

How can you determine if a set of points represents a function?

Back

A set of points represents a function if no two points have the same x-coordinate.

Front

What does it mean for y to be a function of x?

Back

It means that for every value of x, there is exactly one corresponding value of y.

Front

What is a 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

Given the set of points (1, 2), (2, 3), (1, 4), does this represent a function?

Back

No, because the input '1' corresponds to two different outputs (2 and 4).

Front

What is an example of a function?

Back

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

Front

What is the output of the function f(x) = x^2 for x = 3?

Back

The output is 9, since f(3) = 3^2 = 9.

Front

What is an independent variable in a function?

Back

An independent variable is the variable that represents the input values of a function, often denoted as x.