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 the rate of change represent in a function?

Back

The rate of change represents how much the output of a function changes for a given change in the input. It is often calculated as the change in y divided by the change in x.

Front

How do you calculate the rate of change from two points (x1, y1) and (x2, y2)?

Back

Rate of change = (y2 - y1) / (x2 - x1).

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise (change in y) over the run (change in x).

Front

What is the y-intercept of a function?

Back

The y-intercept is the point where the graph of a function crosses the y-axis, represented as (0, y).

Front

How can you determine if two functions have the same rate of change?

Back

Two functions have the same rate of change if their slopes are equal.

Front

What is the equation of a line in slope-intercept form?

Back

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean for a function to be linear?

Back

A function is linear if it can be represented by a straight line on a graph, meaning it has a constant rate of change.

Front

How do you find the slope from a graph?

Back

To find the slope from a graph, select two points on the line, determine the rise and run between them, and calculate the slope as rise/run.

Front

What is a proportional relationship?

Back

A proportional relationship is a relationship between two quantities where the ratio is constant, often represented by a straight line through the origin.