Semester1ReviewKey
You may use a calculator.
1. Explain how you determine if an equation, table, or situation represents a true function or not.
Answers may vary. For a true function, there is a single output for a given input.
2. Explain in your own words what domain and range mean.
Answers may vary. The domain is the set of all possible -values, and the range is the set of all possible yvalues
3. Give the domain and range of the following function:
4
5
:∞, ∞
R: ∞, 5
4. Give the domain on which the graph above is increasing and decreasing.
Increasing Domain:∞, 4
Decreasing Domain:4, ∞
5. Evaluate 4 for the function 5
4 3
6. Complete the table for the following function: 5
2
1
1
4
0
5
1
4
2
1
7. Explain how you would choose inputs for the function √ 6.
Answers may vary. Choose numbers such that when subtracted by 6 the result is a perfect root.
8. Determine the initial value and average rate of change over the interval 2, 2 of the function 5.
R.O.C. = ; I.V. = 5
9. Explain how to determine if an equation represents a linear function. Explain how to determine if a graph
represents a linear function. Explain how to determine if a table represents a linear function.
Answers may vary
Equation: in the form !
Graph: straight line
Table: constant rate of change
Speed (s)
Distance from Home '
10. Draw a graph comparing distance from home to time that matches the story. Then draw a different graph
comparing speed and time that matches the same story.
A boy started at home and slowly walked toward his friend’s house. After a while, he ran as fast as he
could. Once at his friend’s house, he stayed there for the rest of the day.
Time &
Time &
11. Write and solve an equation for the following situation:
Menards is running a sale for $2.50 off each bag of fertilizer. Matt bought 6 bags at the sale price and
also used a coupon for $5 off a $25 purchase. If his total was $55, determine the original price of the bags
of fertilizer.
6 2.50 5 55
$12.50
12. Determine if the given equation accurately represents the situation below. If not, write an accurate
equation and explain why you made the changes you made.
At Walgreens, 20 oz Gatorade bottles usually cost $1.19; however, since Marley is a preferred customer,
she receives a certain amount off each bottle. If she purchased 5 bottles for $4.70. how much was
discounted off each bottle?
=discount
51.19 4.70
51.19 4.70
Explanations may vary. The discount should have been subtracted from the original price
13. Describe in your own words what the inverse of a function is. Describe the process for finding the inverse
of a function.
Answers may vary. An inverse function undoes the original function. The inputs and outputs are switched
in an inverse function. To find the inverse function of an equation, replace with and with and
solve for the new .
14. Find the inverse function of 2
3 6
15. Which rocket has the slowest speed and which rocket has the biggest head start where ( is distance in
feet and is time in seconds? Rocket C is slowest at 20/*; Rocket B with a 10 ft head start
Rocket A
260 feet in 10 seconds with a 5 meter headstart
(
2
45
Rocket C
4
85
6
125
8
165
Rocket D
'
10
205
Rocket B
( 25 10
16. Solve 9 3 11.
4
&
17. Solve 4+ 1 5+ 5 +.
,-*-./0-,
18. Solve 2 2 5 1 15 and graph the solution on a number line.
13
19. Find and explain the mistake(s) in the work below. Then describe how to fix the mistake and find the
correct solution.
2 4 2 2 10
2 4 2 2 10
2 2 2 10
2 4 8 2 10 Distribute first according to order of operations
2 4 2 10
4 6 2 10
2 2 14
4 2 16
2 7
4 4 Change the inequality when dividing by a negative number
20. Graph the inequality 5 4
21. Find the solution to the system of equations by graphing
4 2 6
2 4
2, 1
22. Solve using any method: , 3
3 1
3 2 4
23. Solve using any method: ,-*-./0-,
2 5
4 2 15
24. A 3% solution of acid was mixed with an 18% solution of acid to produce an 8% solution. How much 3%
solution and how much 18% solution were used to produce 15 L of 8% solution?
10 L of 3% solution and 5 L of 18% solution
25. Cauliflower worth $2.25 a pound was mixed with asparagus worth $3.25 a pound to produce a mixture
worth $2.65 a pound. How many pounds of each vegetable were used to produce 35 pounds of the
mixture? 21 pounds of cauliflower and 14 pounds of asparagus
26. Farmer Gena looks out her window and counts a total of 64 legs on a total of 20 animals. If she has only
horses and chickens, how many of each does she have? 12 horses and 8 chickens
27. Graph the system of inequalities:
3 2 8
7
2 5 4
8
8
8
9
28. Determine if the following statement is true or not: 9 √: . False9 ; 8
@
8
@
8
29. Determine if the following statement is true or not: < 8=>? => @. True < 8=>? => @
30. Graph the function 2AB
1
31. Given the parent function 2A , describe the transformation that would take place: 2 ∗ 3
Stretched twice as far from the -axis and translated left 3 units
32. Given the parent function 2A , describe the transformation that would take place: 3 2
Stretched three times as close to the -axis and translated down 2 units
33. The population of the North Arctic penguin is currently 12,900 and decreasing at a rate of 8%. Write the
exponential function that models this situation. D 12,9000.92E
34. Find the solution to the following system of equations:
2A 8
2, 4
7
3 2
3000 lemmings
Lemmings w/ Parachutes (in thousands)
35. The following graph shows the population of lemmings with the evolutionary trait of a parachute. What
was the population in 2006?
Years from 2000