Download Algebra II Quiz 1-1 to 1-3 Mr

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REVIEW Unit 1: Introduction to Algebra 2, Functions
NAME______________________
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
To which sets of numbers does the number belong?
____
1.
a. irrational numbers, real numbers b. rational numbers, irrational numbers c. integers, rational numbers, real
numbers d. whole numbers, integers, rational numbers, real numbers
Insert <, >, or = to make the sentence true.
____
2.
a. < b. > c. =
____
3.
a. = b. > c. <
____
4. Simplify
.
a. –29 b. 29 c. –5 d. 5
Solve the equation.
____
5.
a. 
____
3
1
5
1
b. 2 c. 2 d. 2
7
9
7
3
6.
a. –0.5 b. 0.5 c. –2 d. 2
Solve the equation or formula for the indicated variable.
____
7.
, for t
a.
b.
c.
d.
Graph the number on a number line.
____
8.
a.
b.
–5 –4 –3 –2 –1 0 1 2 3 4 5
–5 –4 –3 –2 –1 0 1 2 3 4 5
c.
d.
–5 –4 –3 –2 –1 0 1 2 3 4 5
–5 –4 –3 –2 –1 0 1 2 3 4 5
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Find the opposite and the reciprocal of the number.
____
9. 0.88
a.
25
25
25 22
22
, 0.88 b. –0.88,
c.
,
d. –0.88,
22
22
22 25
25
Evaluate the expression for the given value of the variable(s).
____
10.
;x=3
a. –11 b. –19 c. –25 d. –30
____
11. The expression
models the height of an object t seconds after it has been dropped from a height of
1500 feet. Find the height of an object after falling for 2.5 seconds.
a. 3100 ft b. 1460 ft c. 1600 ft d. 1400 ft
Simplify by combining like terms.
____
12.
a.
____
b.
c.
d.
13. The sides of a triangle are in the ratio 3 : 4 : 5. What is the length of each side if the perimeter of the triangle is 24
cm?
a. 6 cm, 8 cm, and 10 cm b. 5.1 cm, 6.9 cm, and 8.6 cm c. 2 cm, 6 cm, and 8.6 cm d. 5 cm, 6 cm, and 7 cm
Solve for x. State any restrictions on the variables.
____
14.
a.
;
b.
Solve! Show steps neatly!
15.) 5w + 8 – 12w = 16 – 15w
17.
;
c.
;
16.) 3y + 5 + 4y = 3(2y – 11)
d.
;
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18.
Solve the inequality. Then graph your solution.
19.
20. 5x – (x + 2) > - 5 ( 1 + x) + 3
10  15x  10x  10
21.State the domain and range of each relation. Then state if it is a function or not.
a.
{(4,-7), (-4,-7), (-4,7), (4,7)}
b. {(9,1), (7,2), (5,3), (3,4), (1,5)}
22. Give the relation {(3,2), (5,3),(6,3),(2,1)}
A. Is it discrete or continuous?
B. Domain?
C. Range?
D. Function? Yes or no?
E. Graph the relation:
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23. Give the relation y = 2x - 1
A. Is it discrete or continuous?
E. Graph the relation:
B. Domain?
C. Range?
D. Function? Yes or no?
24. List the four ways to represent a relation.
a. ____________________________
b.
____________________________
c. __________________________
d. __________________________
25. Using the function from problem 23 create a representation of all four (hint: the representation in problem 23 is ordered pairs)
26. (a)
(b)
c)
Complete the following definition. A relation is_____________________.
List four different things wrong with the graph drawn below.
True or false? The graph drawn in part (b) is a relation.
(i)
__________________
(ii)
__________________
(iii)
__________________
(iv)
_________________
___________
(d)
Explain clearly why the graph drawn in part (b) is not a function. You should include a discussion of the Vertical Line Test in your answer that shows you understand the concept.
(e)
Write down the equation of any relation that is a function. Sketch a graph of your equation using good form.
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27.
Let
f  x   x 2  3x  4 .
f  2 showing your steps.
(a)
Evaluate
(b)
Alex thinks that the point
 1, 6 is on the graph of f  x   x 2  3x  4 .
Explain clearly
whether or not Alex is correct.
27. Complete the table below and graph
Function
Describe Changes to the Parent Function
y
Parent Function
x
a) y 
x 4
b) y 
x 4
c) y 
x 3
d) y 
x 2
y
Domain
Range
x0
y0
y
a)
b)
x
c)
x
d)
y
y
x
x
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28. a)
Graph the function
y  f  x   3x  4 on the set of axes below.
y
4
3
2
1
x
0
-5
-4
-3
-2
-1
0
1
2
3
4
5
-1
-2
-3
-4
(b)
Determine the equation of the inverse and graph
y  f 1  x  on the same set of axes.
29. The functions f and g are defined by the following tables.
x
f  x
x
g  x
1
0
2
3
3
1
2
0
1
2
1
3
5
1
1
(a)
Explain why f is a function.
(b)
Explain why g is one-to-one. Why is it advantageous for a function to be one-to-one?
(c)
Use the tables to evaluate each composite function.
(i)
30.
1
f  g 1 
Bob thinks that the inverse of
(ii)
f 1  g 1 
(iii)
g
1
f   1
f  x   3 x  2 is g  x    x  2  . Use algebra to find f  g  x   and
g  f  x   to see whether or not Bob is correct.
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31. Suppose you attended the Olympic Team Finals in Gymnastics. The cost of the ticket was 295 British pounds.
The exchange rate to go from dollars to pounds is modeled by:
D = .64P where D is for dollars and P is for pounds.
a.
Write the inverse function.
b.
Use your inverse function to find the cost of an Olympic ticket in dollars.
c. The exchange rate from dollars to euros is given by:
D = .81E where D is for dollars and E is for euros.
Use this information for dollars, pounds, and euros to write a function to model the exchange
rate from pounds to euros AND euros to pounds.
32. Refer to the area of a circle formula as A = πr 2
a. Fill in the table of the values of a radius of a circle from 1-5 and write the area in terms of pi.
r
Area
1
2
3
4
5
b.
Graph your function below.
c.
Write the inverse of the Area function and leave your answer in terms of pi.
d.
Graph your inverse function on the same coordinate plane as the original function.
e.
Describe how you can graph the inverse of a function without determining the inverse function itself.
Demonstrate by graphing the inverses of the functions below:
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33. Which of the following is most likely represented by this graph?
a. the weight of a desk
b. the amount of gas in a car gas tank during an afternoon drive
c. the outdoor temperature during one morning
d. the amount of birthday cake at a party
e. your speed as you walk uphill
34. . Which of the following is TRUE about a graph of the amount of parking fees collected at the beach and
the daily temperature?___
a. The temperature is the dependent variable.
b. The amount of fees is the independent variable.
c. The y-values range from 0 m to 100 m.
d. The independent variable is temperature.
45.The following table shows the number of years employees have worked and the number of vacation days they
have earned. Use the table for questions a through d.
Years at company
2
4
6
9
11
15
15
Vacation Days
6
10
9
15
14
21
24
a. Make a scatter plot on the grid provided.
b. Determine the correlation.__________
c. Draw a Best Fit Line.
d. Predict the amount of vacation days for an employee who has worked for 25 yrs.
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