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DeSmet - Math 152
Blitzer 5E
∫ 1.1 - Algebraic Expressions and Real Numbers
1. Warm-up: Evaluate 4 − 7 2 + 8 ÷ 2 ( −3)
2
2. Some vocabulary:
(a) Let 2 16x − x 2 represent the number of people surfing Steamer Lane when the waves are x feet
(
)
high.
(i) The “mathematical object” 2 16x − x 2 is called a(n) ______________________________ .
(
)
(ii) Another example of an expression:
(iii) Objects in the above example separated by the + and − signs are called ____________.
The _________ in 7x − 8y 2 +
7x
are:
y7
(iv) What mathematical “things” can we do to expressions?
(
)
(b) Evaluate the expression 2 16x − x 2 for x = 0, 2, 8, 12, and 16 .
What are you finding in terms of waves and surfers?
(
)
(c) Now consider the mathematical “thing” y = 2 16x − x 2 where y is the number of surfers at Steamer
Lane and x is still wave height in feet.
Section 1.1
Pg. 1
DeSmet - Math 152
Blitzer 5E
(
)
(i) What do we call y = 2 16x − x 2 ?
(ii) What can we to with such an equation / formula?
(iii) Fill in the table of values below. Use your table of values to graph the equation. Be sure to label
your axis. Then, pick one point from the graph to interpret (use appropriate values and units).
We say this equation gives a relation between wave height and number of surfers.
y = 2 (16x − x 2 )
x
( x, y )
0
2
4
6
8
10
12
14
16
18
(d) Use your table or your graph to answer the following:
(i) What wave height attracts the most surfers?
(ii) What wave height(s) will attract 120 surfers?
[*what equation are you solving here?]
Section 1.1
Pg. 2
DeSmet - Math 152
Blitzer 5E
3. Evaluating an Expression:
Evaluate the following expression for the indicated variables.
(a)
x 2 − 4 ( x − y ) , for x = 8 and y = 3
(b )
x 2 − y 3 for x = −2 and y = −3
4. Sets of Numbers:
You will be responsible to know the following sets of numbers:
(a) The Set of Integers: {…,−3, − 2, − 1, 0, 1, 2, 3, …}
The squiggly brackets indicate we are speaking about a set of numbers.
⎧a
⎫
a and b are integers and b ≠ 0 ⎬
⎩b
⎭
(b) The Set of Rational Numbers: ⎨
Examples:
(c) The Set of Irrational Numbers: The set of numbers whose decimal representations neither terminate
nor repeat. Irrational numbers cannot be written as quotients of integers.
Examples:
(d) The Set of Real Numbers: The real numbers are all numbers that are either rational or irrational.
These are the numbers we will be dealing with (mostly) in this class!
We can graph them all on the number line (include {0, e, π , 1, 2, 3, − 1, 0.2...} )
(e) The further to the left you live on the number line, the smaller you are.
Are each of the following statements true or false?
Section 1.1
(a)
3 < −2
(d )
− 87 < −1
(b )
( e)
− 2 > −3
0.3 ≥ 0.3
(c)
5≤5
(f)
e>π
Pg. 3