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 definition of domain in a function?

Back

The domain of a function is the complete set of possible values of the independent variable (input) for which the function is defined.

Front

What is the definition of range in a function?

Back

The range of a function is the complete set of possible values of the dependent variable (output) that results from using the function.

Front

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

Back

Not a Function (because the input '1' is associated with two different outputs: '2' and '4').

Front

Identify the function from the following sets: (1,2), (2,3), (3,4), (4,5)

Back

(1,2), (2,3), (3,4), (4,5) (This is a function as each input has a unique 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 a vertical line intersects the graph at more than one point, then it is not a function.

Front

Given f(x) = 2x + 3, find f(2).

Back

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

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if it never assigns the same value to two different domain elements.

Front

What is the output of g(x) = x^2 when x = -3?

Back

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

Front

What is the difference between independent and dependent variables in a function?

Back

The independent variable is the input of the function (often x), while the dependent variable is the output (often y) that depends on the input.