General Mathematics Test Preparation: Key Concepts and Techniques
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Course
CE 101
Institution
University Of San Carlos
Prepare for your first mastery test with this thorough summary of general mathematics concepts. Covering relations and functions, piecewise functions, and operations on functions, this PDF provides clear explanations, illustrative examples, and practical exercises. Ideal for high school and college...
I. CONCEPTS OF RELATIONS AND FUNCTIONS
a. Terminologies
b. Different Representations of Functions
c. Determine if the given is Function or Not
d. Evaluation of functions
II. PIECEWISE FUNCTION
a. Definition
b. Evaluation of functions
III. OPERATIONS ON FUNCTIONS
I. CONCEPTS OF RELATIONS AND FUNCTIONS
A. TERMINOLOGIES
1. ORDERED PAIR- a composition of x-coordinate(abscissa) and y-coordinate(ordinate) which is written in
parentheses
2. DOMAIN – set of all first components ( x-values, input, independent values)
3. RANGE – set of all second components (y -values, output, dependent values)
4. RELATION – any set of ordered pairs
5. FUNCTION- a special type of relation in which each member of domain corresponds to exactly one member of
the range
B. DIFFERENT REPRESENTATIONS of RELATIONS and FUNCTIONS
1. SET OF ORDERED PAIRS
ILLUSTRATIVE EXAMPLES:
Find the domain and range of each of the following set of ordered pairs and determine whether it is a FUNCTION or NOT.
a. {(-6,-7),(3,2),(8,-7),(10,8)} b. {(1,3),(1,4),(1,5),(1,6)}
SOLUTIONS:
a. Domain (set of x-values): {-6,3,8,10} b. Domain: {1}
Range (set of y-values) : {-7,2,8,} Range : {3,4,5,6}
This is a FUNCTION since the x-values are different. This is NOT a FUNCTION since there is only one x-value
which is 1.
Note: Always use braces { } to indicate the set for Domain and Range.
Write the value once. There must be no repetition in writing the same value.
2. TABLE
ILLUSTRATIVE EXAMPLES:
Find the domain and range of each and determine whether it is a FUNCTION or NOT.
a.
X Y SOLUTION:
-3 4
4 3 a. Domain (set of x-values): {-3,4,5,6,3}
5 6 Range (set of y-values) : {4,3,6,5}
6 3
, b.
X Y SOLUTION:
-2 -6 Domain (set of x-values): {-2,-3,-4}
-3 2 Range (set of y-values) : {-6,2,3,4}
-3 3
-4 4 This is NOT a FUNCTION since there is a repetition of the x-value which is -3.
3. MAPPING
ILLUSTRATIVE EXAMPLES:
Find the domain and range of each and determine whether it is a FUNCTION or NOT.
a.
INPUT OUTPUT
SOLUTION:
-7 -3 {(-7,2),(2,1),(3,-3)}
Domain (set of x-values): {-7,2,3}
2 2 Range (set of y-values) : {-3,2,1}
3 1 This is a FUNCTION since the x-values are different.
b.
INPUT OUTPUT
SOLUTION:
-6 {(-8,-4),(-8,2),(0,-6),(2,4)}
-8
-4 Domain (set of x-values): {-8,0,2}
0
Range (set of y-values) : {-6,-4,2,4}
2
2
4 This is NOT a FUNCTION since there is a repetition of the x-value which is -8.
4.EQUATION
ILLUSTRATIVE EXAMPLES:
Determine whether the following equations is a FUNCTION or NOT.
1. 𝑦 = 3𝑥 − 2
FUNCTION since the exponent in the y variable is odd which is 1.
2. 𝑥 3 + 3𝑦 2 = 7
NOT a FUNCTION since the exponent in the y variable is even which is 2.
3. 4𝑦 4 = 3𝑥 − 1
NOT a FUNCTION since the exponent in the y variable is even which is 4.
4. 5𝑥 2 + 2𝑦 3 = 1
FUNCTION since the exponent in the y variable is odd which is 3.
5. f(x)= √𝑥 + 3
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