Comparing Functions

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. It can be represented as an equation, a graph, or a table.

Front

What does 'rate of change' mean in a function?

Back

The rate of change describes how much the output of a function changes for a given change in the input. It is often represented as the slope in linear functions.

Front

How do you find the slope of a linear function?

Back

The slope (m) can be found using the formula m = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are two points on the line.

Front

What is the initial value of a function?

Back

The initial value is the output of the function when the input is zero. In the equation y = mx + b, it is represented by b.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form y = mx + b.

Front

What is a non-linear function?

Back

A non-linear function is a function that does not graph to a straight line. Its rate of change varies and can be represented by curves.

Front

How can you tell if a function is increasing or decreasing?

Back

A function is increasing if the output values rise as the input values increase, and decreasing if the output values fall as the input values increase.

Front

What is the difference between a function and a relation?

Back

A relation is any set of ordered pairs, while a function is a specific type of relation where each input is associated with exactly one output.

Front

What does it mean for a function to have a constant slope?

Back

A function has a constant slope if the rate of change is the same between any two points on the line, indicating a linear relationship.

Front

How do you identify the greatest initial value among functions?

Back

To identify the greatest initial value, compare the y-intercepts (b values) of the functions in their linear equations.