Download Math 150 Practice Problems – Rule of Four, Number System, Sets

F12-M150
Rule of four, No. Sys, Sets, Abs. val
9/3/2012
Math 150
Practice Problems – Rule of Four, Number System, Sets, Absolute Value
The Rule of Four:
1. Given 𝑦 = 2𝑥 3
a) Which form of representation is this out of the four rules to describe a
mathematics problem?
b) What are the other forms? Write the names and appropriate
representation for the given problem.
c) Sketch the graph for = 2(𝑥 − 1)3 .
2. Anna and Sana are two sisters. Sana is three years older than Anna.
a) Which form of representation is this out of the four rules to describe a
mathematics problem?
b) What are the other forms? Write their names and appropriate
representation for the given problem. Make the necessary assumptions.
(Let 𝑥 represent Anna’s age, and let 𝑦 represent Sana’s age).
c) What are the slope and 𝑦 −intercept of the line.
d) How would the graph be if they were both the same age.
e) What are the slope and 𝑦 −intercept of the new graph.
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F12-M150
Rule of four, No. Sys, Sets, Abs. val
9/3/2012
Number System
3. Consider the following numbers. Which sets of the number system do these
numbers belong to :
Natural
numbers
Whole
Numbers
Integers
Rational
Numbers
Irrational
Numbers
Real
107
29575
2
3
6
-5
0
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2.31572… 3.5123
Sets
4. Write the inequality and/or interval notation as applicable:
a) 𝑥 ∈ (−5, −1) ∪ [0,7]
b) 𝑥 ∈ (−∞, 1) ∪ (2, 5]
c) 𝑥 ∈ (0, ∞)
d) Set of real numbers less than 10 AND greater than -5
e) Set of real numbers less than or equal to 10 AND greater than or equal
to -5.
f) Set of real numbers greater than 10 and less than -5.
g) 0 ≤ 𝑥 ≤ 25
h) −7 ≤ 𝑥 ≤ 7
i) Set of real numbers greater than 2 and greater than or equal to 10.
j) Set of all real numbers
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F12-M150
Rule of four, No. Sys, Sets, Abs. val
9/3/2012
Absolute Value
5. Find the solution to the equations :
a) 𝑥 2 = 16
b) |𝑥 + 4| = 3
c) |𝑥| = 𝑥 − 1
d) 4|𝑥 − 3| = 2
e) 3|𝑥 − 5| + 1 = 7
f) |𝑥 − 1| = 2𝑥 + 3
g) |2𝑥 + 4| = −3𝑥 − 1
h) (𝑥 − 1)2 = 9
6. For the following, recognize the ‘c’ and ‘d’ , find the solution, sketch and
write the solution in interval and inequality notation.
a) |𝑥 + 3| > 4
b) |𝑥 + 4| < 2
c) |𝑥 − 5| ≥ 3
d) |𝑥 − 4| < 3
e) |𝑥 + 3| = 2
7. For each of the following, sketch the solution and write it in the form of
absolute value inequality equation:
a) 𝑥 ∈ (1,7)
b) 𝑥 ∈ [−3,5]
c) 2 ≤ 𝑥 ≤ 8
d) 𝑥 > 5 𝐴𝑁𝐷 𝑥 < −1
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