4.5 Comparing Functions

Front

What is the rate of change in a function?

Back

The rate of change in a function is a measure of how much the output value (y) changes for a given change in the input value (x). It is often represented as the slope of the line in a linear function.

Front

How do you find the rate of change from a table of values?

Back

To find the rate of change from a table of values, calculate the difference in the output values (y) divided by the difference in the input values (x) for two points.

Front

What is the equation of a linear function?

Back

The equation of a linear function is typically written in the form y = mx + b, where m is the slope (rate of change) and b is the y-intercept.

Front

If Nate's service is described by y = 4x + 6, what is the rate of change?

Back

The rate of change for Nate's service is 4, meaning for each additional movie, the cost increases by $4.

Front

How do you compare two linear functions?

Back

To compare two linear functions, analyze their slopes (rates of change) and y-intercepts. The function with the greater slope has a higher rate of change.

Front

What does it mean if two functions have the same rate of change?

Back

If two functions have the same rate of change, they increase or decrease at the same rate, but they may have different starting points (y-intercepts).

Front

What is a y-intercept?

Back

The y-intercept is the point where a line crosses the y-axis, representing the output value when the input value (x) is zero.

Front

How can you determine which service is cheaper using equations?

Back

To determine which service is cheaper, substitute the same input value (e.g., number of movies) into both equations and compare the output values (costs).

Front

What is the significance of a higher setup fee in a service?

Back

A higher setup fee indicates a larger initial cost before any services are rendered, which can affect the overall cost-effectiveness of the service.

Front

How do you interpret the slope of a line in a real-world context?

Back

The slope of a line in a real-world context represents the rate of change, such as cost per item or speed, indicating how one quantity changes in relation to another.