Relations, Functions, and Linear Functions

Front

What is a function?

Back

A function is a relation where each input (x-value) has exactly one output (y-value).

Front

What is the definition of a relation?

Back

A relation is a set of ordered pairs, where each pair consists of an input and an output.

Front

How can you determine if a table represents a function?

Back

A table represents a function if no x-value is repeated with a different y-value.

Front

What is the difference between input and output in a function?

Back

Input is the value you put into a function (x-value), while output is the value you get out (y-value).

Front

What does the term 'dependent variable' mean?

Back

The dependent variable is the output of a function, typically represented as y, which depends on the input (x).

Front

What is an independent variable?

Back

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

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.

Front

What does the slope (m) represent in a linear function?

Back

The slope (m) represents the rate of change of the function, indicating how much y changes for a unit change in x.

Front

What does the y-intercept (b) represent in a linear function?

Back

The y-intercept (b) is the point where the line crosses the y-axis, representing the output when x = 0.

Front

How do you write the equation of a linear function?

Back

The equation of a linear function can be written in the form y = mx + b, where m is the slope and b is the y-intercept.