Functions and Function Notation

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 function notation?

Back

Function notation is a way to denote functions using symbols, typically written as f(x), where f is the function name and x is the input.

Front

What does the vertical line test determine?

Back

The vertical line test determines if a graph represents a function. If a vertical line intersects the graph at more than one point, it is not a function.

Front

What are the domain and range of a function?

Back

The domain is the set of all possible input values (x-values) for a function, while the range is the set of all possible output values (y-values).

Front

What is an independent variable?

Back

The independent variable is the input of a function, often represented by x, which can be freely chosen.

Front

What is a dependent variable?

Back

The dependent variable is the output of a function, often represented by y, which depends on the value of the independent variable.

Front

What is the difference between inputs and outputs in a function?

Back

Inputs are the values you put into a function (x-values), while outputs are the values you get out of a function (y-values).

Front

Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, but each input must correspond to only one output.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, represented by the equation y = 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 expressed in the form y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.