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.

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).

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.

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.

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.

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.

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.

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.

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.

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.