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 vertical line test?

Back

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

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

If f(x) = 3x - 2, what is f(2)?

Back

f(2) = 3(2) - 2 = 6 - 2 = 4.

Front

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

Back

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

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, typically in the form f(x) = mx + b.

Front

If f(x) = x^2, what is f(-3)?

Back

f(-3) = (-3)^2 = 9.

Front

What is an example of a non-function?

Back

An example of a non-function is the relation {(1, 2), (1, 3)}, where the input 1 is associated with two different outputs.

Front

What is a constant function?

Back

A constant function is a function that always returns the same value, regardless of the input, e.g., f(x) = 5.