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 change in the input value (x). It is often represented as the slope of the line in a linear function.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

How do you calculate the slope of a line?

Back

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

Tags

CCSS.8.EE.B.5

Front

What does a positive slope indicate?

Back

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

Tags

CCSS.8.EE.B.5

Front

What does a negative slope indicate?

Back

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

Tags

CCSS.8.EE.B.5

Front

What is a constant rate of change?

Back

A constant rate of change means that the change in the output value is consistent for equal changes in the input value, characteristic of linear functions.

Tags

CCSS.HSF-LE.A.1B

Front

What is the difference between rate of change and slope?

Back

The rate of change refers to how one quantity changes in relation to another, while slope specifically refers to the steepness of a line on a graph, representing the rate of change.

Tags

CCSS.8.EE.B.5

Front

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

Back

To compare the rates of change, calculate the slope of each function and determine which slope is greater or if they are equal.

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

Front

What is the significance of a slope of zero?

Back

A slope of zero indicates a horizontal line, meaning there is no change in the output value regardless of changes in the input value.

Tags

CCSS.8.EE.B.5

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 are parallel lines and will never intersect, indicating they have a consistent relationship.

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

Front

How do you interpret a slope of 1?

Back

A slope of 1 means that for every unit increase in x, the y-value increases by the same amount, indicating a direct one-to-one relationship.

Tags

CCSS.8.EE.B.5