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 (dependent variable) changes for a given change in the input value (independent variable). 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 determine which function has the greatest rate of change?

Back

To determine which function has the greatest rate of change, compare the slopes of the functions. The function with the highest slope value (steepest incline) has the greatest rate of change.

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

Front

What is the significance of slope in a linear function?

Back

The slope of a linear function indicates the rate of change of the dependent variable with respect to the independent variable. A positive slope indicates an increasing function, while a negative slope indicates a decreasing function.

Tags

CCSS.8.EE.B.5

Front

How do you calculate the slope between two points on a graph?

Back

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

Tags

CCSS.8.EE.B.5

Front

What does a slope of -5/4 indicate about a function?

Back

A slope of -5/4 indicates that for every 4 units the x-value increases, the y-value decreases by 5 units. This represents a decreasing linear function.

Tags

CCSS.8.EE.B.5

Front

What is a function in mathematical terms?

Back

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

Tags

CCSS.8.F.A.1

Front

What is the difference between a linear function and a non-linear function?

Back

A linear function has a constant rate of change and can be represented by a straight line on a graph, while a non-linear function has a variable rate of change and is represented by a curve.

Tags

CCSS.8.F.A.3

Front

What is the formula for calculating the cost per guest in a party planning scenario?

Back

The cost per guest can be calculated by dividing the total cost (initial fee plus additional fees based on the number of guests) by the number of guests.

Tags

CCSS.7.EE.B.4A

Front

How can you compare the costs of different party coordinators?

Back

To compare the costs of different party coordinators, calculate the total cost for a specific number of guests for each coordinator and then compare the results.

Tags

CCSS.8.EE.B.5

Front

What is the importance of understanding rates of change in real-world applications?

Back

Understanding rates of change is crucial in real-world applications as it helps in making informed decisions, such as budgeting, planning, and analyzing trends.

Tags

CCSS.HSF-LE.A.1B