Comparing Functions

Front

What is the rate of change in a function?

Back

The rate of change in a function, often represented as the slope, measures how much the output (y) changes for a change in the input (x). It is calculated as the change in y divided by the change in x.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Tags

CCSS.8.EE.B.5

Front

What does a positive slope indicate about a function?

Back

A positive slope indicates that as the input (x) increases, the output (y) also increases.

Tags

CCSS.8.EE.B.5

Front

What does a negative slope indicate about a function?

Back

A negative slope indicates that as the input (x) increases, the output (y) decreases.

Tags

CCSS.8.EE.B.5

Front

What does a slope of zero indicate?

Back

A slope of zero indicates that the function is constant; there is no change in y as x changes.

Tags

CCSS.8.EE.B.5

Front

What is the significance of comparing slopes in real-world scenarios?

Back

Comparing slopes helps determine which situation has a greater rate of change, which can be crucial in fields like economics, physics, and engineering.

Tags

CCSS.8.EE.B.5

Front

If Smith's rate of change is 5/4 and Harmon's is 7/2, who has the greater rate of change?

Back

Harmon has the greater rate of change with 7/2.

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

Front

If Casey's rate of change is greater than Hunter's, what can we conclude?

Back

Casey has a higher rate of change compared to Hunter, indicating a steeper slope in the context of their functions.

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

Front

How do you interpret a slope of 100 in a real-world context?

Back

A slope of 100 means that for every unit increase in x, y increases by 100 units, indicating a very steep increase.

Tags

CCSS.8.EE.B.5

Front

What is the difference in rates of change between Ryan's Rafts and Water's Edge Rafts if Ryan's is $15 per hour?

Back

Water's Edge Rafts charges $3.75 more per hour than Ryan's Rafts.

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9