Download Unit 1 Study Guide Foundations for Functions NAME: DATE: In this

Unit 1 Study Guide
Foundations for Functions
NAME:____________________________________________________
DATE:________________
In this study guide, you will find a list of the topics that will be covered on the Unit 1 Test, as well as a
BRIEF summary of the topic and sample test questions. This is meant to help GUIDE your STUDY for the
test, not provide you with ALL of the test questions or give you answers to the test. In addition to
completing this packet, you should also review your notes and graded assignments as well as re-watch
the video lessons for extra help.
THIS PACKET IS WORTH 100 HOMEWORK POINTS AND
IS DUE ON THE DAY OF THE TEST!!!
Unit 1 Topics:
A) Comparing and ordering real numbers
B) Evaluating expressions using substitution
C) Simplifying algebraic expressions by combining like terms and using the distributive property
D) Simplifying radical expressions/square roots using all operations
E) Simplifying expressions using the properties of exponents
F) Identifying whether a relation is a function
G) Using function notation
H) Performing transformations of functions
Section I: Comparing Numbers, Evaluating Expressions, Simplifying Algebraic Expressions
Comparing numbers: You should be able to put numbers in order from least to greatest or compare the value of
two numbers, including negatives.
SAMPLE PROBLEM
If 2 < x < 6, which of the following has the greatest value?
A)
x
B)
x 1
C)
x2
D)
x 1
E)
x2
Evaluating Expressions: You should be able to use substitution to evaluate an expression for a given value.
SAMPLE PROBLEM
What is the value of 7z2 + 4 • 3w when w= 8 and z= -3?
A) 1608
B) 537
C) 412
D) 159
E) -4068
Simplifying Expressions: You should be able to simplify an algebraic expression by combining like terms. Like
terms must have the SAME variable with the SAME exponent. Like terms can also be constant terms, or numbers
without variables. You should also be able to use the distributive property, by multiplying the outside value to
anything inside the parenthesis. Ex. 2(3x + 5) = 6x + 10
SAMPLE PROBLEM
Which expression is equivalent to x 2  3 x ?
A) 2( x 2  x)  3x 2  5x
B) 2( x 2  x)  3x 2  5x
C)  2( x 2  x)  3x 2  5x
D)  2( x 2  x)  3x 2  5x
Section II: Square Roots
You should be able to perform all operations on square roots (addition, subtraction, multiplication and division).
You should be able to simplify square roots completely and rationalize the denominator, if necessary.
SAMPLE PROBLEMS
Which expression is in simplest form?
A)
45  3 5
B)
2  10
D) 4 30
D)
27
9
Which expression can be used to represent the area of the rectangle shown?
a) 8 3
b) 2 8
c) 4 8
d) 2 12
8
24
Simplify each expression using the properties of square roots.
A) 2 2  72
B)
72
4
C) 3 10  2
D)
5 125
3
Section III: Properties of Exponents
You should be able to use the properties of exponents to simplify expressions.
Properties of Exponents:
A) When you multiply powers, add the exponents.
B) When you divide powers, subtract the exponents.
C) When you raise a power to a power, multiply the exponents.
D) Anything to the zero power equals ONE.
E) When you have a negative exponent, flip the term with the negative exponent to the opposite part of the
fraction, then make the exponent positive.
SAMPLE PROBLEMS
Which of the following is not equivalent to
a) m 2 n11
b)
m 4 n12
m2n
( mn3 ) 4
?
m2n
c) m 1 n11
d) (mn3 ) 4 m 2 n 1
e) m 2
(n 3 ) 4
n
Which expression is equivalent to  (5 x 2 y 1 z 3 ) 2 ?
A) 
5x 4
y2z6
B) 25 x 4 y 2 z 6
C)  25 x 4 y 2 z 6
D) 
25 x 4
y2z6
What is of the volume of the cube shown?
(***V= Length * Width* Height)
3d4
The table below shows the populations of select cities around
the world.
City
Country
Population
Houston, TX
United States
1.953 x 106
Seoul
South Korea
1.023 x 107
Hong Kong
China
6.843 x 106
Chicago, IL
United States
2.896 x 106
Cairo
Egypt
6.800 x 106
Istanbul
Turkey
8.260 x 106
What statement is true about the values
shown?
A) The cities are arranged by least
population to greatest population.
B) Istanbul has the greatest population
out of all of the cities shown in the table
C) Chicago has a greater population than
Soeul
D) Hong Kong has a smaller population
than Istanbul
Section IV: Functions
You should be able to:
-Identify the domain (x-values) and range (y-values) of a function
-Identify whether a relation is a function (if any of the inputs repeat with different outputs, it is NOT a function!)
-Use function notation ie f(x)
-Perform transformations of functions
A) Translation: Slide left, right, up or down
B) Reflection: Flip over a line of reflection
C) Stretch: Expand the figure
D) Compress: Shrink the figure
SAMPLE PROBLEMS
Which element is in the range of the function {(-9, -2), (2, 4), (3, -7), (8, 1), (10, 0), (5, 6)}?
A) -9
B) -1
C) 2
D) 3
E) 6
Consider the function f(x) = 6x – 12. What is f(-3)?
A) -216
B) -30
C) -18
D) -6
For which function does f(-8)= -6?
A) f ( x)  2 x 2  6
B) f ( x)  10 x  6
C) f ( x)  x 2  10
D) f ( x)  2 x  10
Refer to the table below. If the milk price is the range and the number of ounces is the domain, which statement is
true for the graph of the data in the table?
Package Size
Number of Ounces
Milk Price
1 pint
16
$0.90
1 quart
32
$1.29
1 half gallon
64
$1.95
2 quarts
64
$2.58
1 gallon
128
$3.90
A)
B)
C)
D)
The graph is a function
The points form a line
The graph fails the vertical line test
“Milk Price” is the label for the horizontal axis
For what value of x would the relation NOT be a function?
x
y
12
132
15
150
x
132
21
300
A)
B)
C)
D)
15
21
132
12
A phone company charges $40 per month for the first 500 minutes plus $0.75 for each additional minute used.
The expression c(m)= 40 + 0.75m can be used to find the total monthly bill. What would an input of 30 represent
in this situation?
A) 30 minutes have been used this month
B) The monthly bill is $30
C) 530 minutes have been used this month
D) The monthly bill was $530
The function c(p) = 0.99p represents the cost in dollars of p pounds of peaches. If the cost per pound increases by
10%, how will the graph of the function change?
A) Translation 0.1 unit up
B) Translation 0.1 unit right
C) Horizontal stretch by a factor of 1.1
D) Vertical stretch by a factor of 1.1
Which transformation would change the point (5, 3) into (-5, 3)?
A) Reflection across the x-axis
B) Translation 5 units down
C) Reflection across the y-axis
D) Translation 5 units left