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Back to Tutor Intake Assessment: Calculate average rate of change

HSF.IF.B.6 Tutor Intake — Average Rate of Change

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Grade 9·11 problems·~14 min·Common Core Math - HS Functions·group·hsf-if-b-6
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A

Concepts

1.

The average rate of change of a function ff over the interval [a,b][a, b]
is defined as which of the following?

2.

The average rate of change of ff over [a,b][a, b] equals the slope of
which geometric object?

3.

For a linear function, the average rate of change computed over any
interval is always   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   (constant / variable / zero).

blank-1:
B

Procedures

1.

Let f(x)=x2+3f(x) = x^2 + 3.

Calculate the average rate of change of ff from x=1x = 1 to x=4x = 4.

2.

Let h(t)=−16t2+64t+4h(t) = -16t^2 + 64t + 4.

Calculate the average rate of change of hh from t=1t = 1 to t=3t = 3.

3.

The table below shows the height (in inches) of a sunflower plant.

WeekHeight (in)
02
28
418
630
838
1042

What is the average rate of change of height from week 4 to week 8?

4.

A student wants to find the average rate of change of g(x)=2x+5g(x) = 2x + 5
from x=1x = 1 to x=4x = 4. They compute:

g(1)−g(4)4−1=7−133=−63=−2\frac{g(1) - g(4)}{4 - 1} = \frac{7 - 13}{3} = \frac{-6}{3} = -2

The correct answer is +2+2. What error did the student make?

5.

A student is asked for the average rate of change of temperature from
6 AM to noon. The temperature at 6 AM was 54°F and at noon was 72°F.
The student answers "72°F." What is wrong with this answer?

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