4.1 - 4.3: Functions and Function Notation

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. In other words, for every x-value, there is one and only one corresponding y-value.

Front

What is function notation?

Back

Function notation is a way to represent functions using symbols. For example, f(x) represents the function f evaluated at x.

Front

How do you determine if a graph represents a function?

Back

A graph represents a function if any vertical line drawn through the graph intersects it at most once. This is known as the vertical line test.

Front

What does f(8) mean?

Back

f(8) means the output of the function f when the input is 8. It is the value of the function at x = 8.

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

What is a linear function?

Back

A linear function is a function that can be represented by a straight line on a graph. Its general form is f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is a quadratic function?

Back

A quadratic function is a function that can be represented by a parabola on a graph. Its general form is f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

What is the difference between independent and dependent variables?

Back

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

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. This means each output is paired with exactly one input.