Comparing Functions

Front

What is the rate of change in a function?

Back

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

Front

How do you calculate the slope of a line?

Back

The slope of a line is calculated by taking the difference in the y-values (rise) and dividing it by the difference in the x-values (run) between two points on the line: slope (m) = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a function?

Back

A positive slope indicates that as the input value (x) increases, the output value (y) also increases, showing a direct relationship between the two variables.

Front

What does a negative slope indicate about a function?

Back

A negative slope indicates that as the input value (x) increases, the output value (y) decreases, showing an inverse relationship between the two variables.

Front

What is the significance of a slope of zero?

Back

A slope of zero indicates that the function is constant; there is no change in the output value (y) regardless of changes in the input value (x).

Front

What is the meaning of 'rate of change' in real-world applications?

Back

In real-world applications, the rate of change can represent various scenarios, such as speed (distance over time), cost per item, or growth rates, helping to understand how one quantity changes in relation to another.

Front

How can you compare the rates of change between two functions?

Back

To compare the rates of change between two functions, calculate the slopes of both functions and compare their values. The function with the higher slope has a greater rate of change.

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, where m is the slope and b is the y-intercept.

Front

What is the y-intercept of a function?

Back

The y-intercept of a function is the point where the graph of the function crosses the y-axis, which occurs when the input value (x) is zero.

Front

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

Back

In a real-world context, the slope can represent the rate at which one quantity changes in relation to another, such as the cost per week or the speed of an object.