Section 2.4 Homework

1.  If you travel 500 miles in two hours, then your average speed for the trip is  _____ mi/hr

2.  The average rate of change of a function f(x) = x² between x = 1 and x = 7 is 

Average rate of change =

3.  The graph of a function is given. 

(a) Determine the net change between the indicated points on the graph.

(b) Determine the average rate of change between the indicated points on the graph.

4.  The graph of a function is given. 

(a) Determine the net change between the indicated points on the graph.

(b) Determine the average rate of change between the indicated points on the graph.

5. The graph of a function is given. 

(a) Determine the net change between the indicated points on the graph.

(b) Determine the average rate of change between the indicated points on the graph.

6.  A function is given. 

$r\left(t\right) = 4 – \frac{1}{4}t; t=4, t=8$

(a) Determine the net change between the given values of the variable.

(b) Determine the average rate of change between the given values of the variable.

7. A function is given. 

$f\left(z\right)=2–5z^2$

; z=-2, z=0

(a) Determine the net change between the given values of the variable.

(b) Determine the average rate of change between the given values of the variable.

8. A function is given. 

$g\left(t\right)= t^{4–}{t}^3+t^2; t=–3, t=3$

(a) Determine the net change between the given values of the variable.

(b) Determine the average rate of change between the given values of the variable.

9. A function is given. 

$f\left(x\right) = 4–3x^2; x=2, x=2+h$

(a) Determine the net change between the given values of the variable. 

(b) Determine the average rate of change between the given values of the variable. 

10. A function is given. 

$g\left(x\right)=\frac{8}{x}; x=1, x=a$

(a) Determine the net change between the given values of the variable.

(b) Determine the average rate of change between the given values of the variable.

11. A function is given. 

$f\left(t\right)=4\sqrt{t}; t=a, t=a+h$

(a) Determine the net change between the given values of the variable. 

(b) Determine the average rate of change between the given values of the variable. 

12. A linear function is given. 

$f\left(x\right)=\frac{1}{2}x+6$

(a) Find the average rate of change of the function between x = a and x = a + h.

(b) Find the slope of the line. 

13.  The graphs of the functions f and g are shown. The function ___ has a greater average rate of change between x = 0 and x = 1. The function ___ has a greater average rate of change between x = 1 and x = 2. The functions f and g have the same average rate of change between x = ___ and x = ___ .

14. The graph given below shows the population P in a small industrial city from 1950 to 2000. The variable x represents the number of years since 1950. 

(a) What was the average rate of change of P between x = 20 and x = 40?

(b) Interpret the value of the average rate of change that you found in part (a).

1. The population increased during that time span.
2. The population decreased during that time span.    
3. The population did not experience any change during that time span.
4. The population increased and decreased the same amount during that time span.

15. Two speed skaters, A and B, are racing in a 500-m event. The graph shows the distance they have traveled as a function of the time from the start of the race. 

(a) Who won the race? 

1. Skater A
2. Skater B

(b) Find the average speed during the first 10 s for each skater. 

Skater A =

Skater B =

(c) Find the average speed during the last 15 s for each skater. (Round each answer to the nearest whole number.) 

Skater A =

Skater B =