Average Rate of Change Assignment

Front

What is the average rate of change?

Back

The average rate of change of a function over an interval is the change in the function's value divided by the change in the input value over that interval. It is calculated as \( \frac{f(b) - f(a)}{b - a} \) where \( a \) and \( b \) are the endpoints of the interval.

Tags

CCSS.HSF.IF.B.6

CCSS.8.F.B.4

Front

How do you calculate the average rate of change from a graph?

Back

To calculate the average rate of change from a graph, identify two points on the graph, \( (x_1, y_1) \) and \( (x_2, y_2) \). Use the formula \( \frac{y_2 - y_1}{x_2 - x_1} \) to find the average rate of change.

Tags

CCSS.HSF.IF.B.6

CCSS.8.F.B.4

Front

What is the average rate of change of a function represented by a linear equation?

Back

For a linear function, the average rate of change is constant and equal to the slope of the line, which can be calculated as \( \frac{\Delta y}{\Delta x} \).

Tags

CCSS.HSF.IF.B.6

CCSS.8.F.B.4

Front

If a climber is at 400 feet after 2 hours and 700 feet after 6 hours, what is the average rate of change?

Back

The average rate of change is \( \frac{700 - 400}{6 - 2} = \frac{300}{4} = 75 \) feet per hour.

Tags

CCSS.HSF.IF.B.6

CCSS.8.F.B.4

Front

What does a negative average rate of change indicate?

Back

A negative average rate of change indicates that the function's value is decreasing over the interval.

Tags

CCSS.HSF.IF.B.6

CCSS.8.F.B.4

Front

How do you find the average rate of change from a function?

Back

To find the average rate of change from a function \( f(x) \) over the interval \( [a, b] \), use the formula \( \frac{f(b) - f(a)}{b - a} \).

Tags

CCSS.HSF.IF.B.6

CCSS.8.F.B.4

Front

What is the average rate of change of the price of gold from 2000 to 2022 if it was $279.29 in 2000 and $1868.8 in 2022?

Back

The average rate of change is \( \frac{1868.8 - 279.29}{2022 - 2000} = \frac{1589.51}{22} \approx 72 \) dollars per year.

Tags

CCSS.HSF.IF.B.6

CCSS.8.F.B.4

Front

What is the average rate of change of a quadratic function?

Back

The average rate of change of a quadratic function over an interval can be calculated using the same formula as for linear functions, but the value will vary depending on the specific points chosen.

Tags

CCSS.HSF.IF.B.6

CCSS.8.F.B.4

Front

If a ball's height is given by \( h(t) = -2t^2 + 34 \), how do you find the average rate of change between 0 and 4 seconds?

Back

Calculate \( h(0) \) and \( h(4) \), then use the formula \( \frac{h(4) - h(0)}{4 - 0} \). The average rate of change is \( -8 \) meters per second.

Tags

CCSS.HSF.IF.B.6

CCSS.8.F.B.4

Front

What is the average rate of change of a function that decreases from 600 gallons to 525 gallons over 5 minutes?

Back

The average rate of change is \( \frac{525 - 600}{5 - 0} = \frac{-75}{5} = -15 \) gallons per minute.

Tags

CCSS.HSF.IF.B.6

CCSS.8.F.B.4