Advanced Algebra and Trigonometry: Section 2.2: Functions
Finding the zeros
Finding the zeros:
A zero is when f(x) = 0. Also referred to as the roots or x-intercepts.
Find all real values of x such that f(x) = 0.
1. f ( x ) = 7 3x
2. f ( x ) =
3x 4
5
3.
Advanced Algebra and Trigonometry: Section 2.2: Functions Finding the domain
n
stuff stuff 0 when n is even
1 var iable 0 var iable
Find the domain of the function. Write answers in interval notation. 1. f (x) = 5x 2 + 2x - 1 2. f (x) =
4 x
3. f (x) = x -
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Advanced Algebra and Trigonometry: Section P.5
Domain and Simplifying Rational Expressions
Domain: the set of real number for which an algebraic expression is dened.
In non-math words: all the values that you are allowed to plug in
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Advanced Algebra and Trigonometry: Section P.5:
Multiplying and Dividing Rational Expressions
Multiplying:
Step 1: Factor numerators and denominators
Step 2: Look to simplify (up and down, or cross. DO NOT SIMPLIFY SIDE TO SIDE)
Ste
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Advanced Algebra and Trigonometry: Section P.5: Adding and Subtraction Rational Expressions With Like Denominators
When adding and subtracting rational expressions, you need the same denominator. Steps: 1. Find a common denominator,
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Advanced Algebra and Trigonometry: Section P.5: Mixed Expressions and Complex Fractions
Mixed Expressions: The sum or difference of a monomial and a rational expression. Find the common denominator Combine numerators Simplify
1. 3 +
Advanced Algebra and Trigonometry: Section 2.2: Functions
A function is a relation in which each element in the domain corresponds to one
element in the range.
Function Notation:
When an equation is used to represent a function, it is convenient to name
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Factoring Sum or Difference of Two Cubes
a 3 + b 3 = (a + b )(a 2 ab + b 2 )
a 3 b 3 = (a b )(a 2 + ab + b 2 )
Factor:
1. x 3 27
2. y 3 + 8
3. 3x 3 + 192
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Factoring Perfect Square Trinomials
Factor:
x 2 + 14 x + 49
(
Special Formula:
)(
)
a 2 + 2 ab + b 2 = (a + b )(a + b ) = (a + b )2
a 2 2 ab + b 2 = (a b )(a b ) = (a b )2
1.
25 x 2 30 x + 9
3.
a 2 24 a + 144
2.
49 y 2 + 42 y + 36
4
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Factor by Grouping
When there are FOUR terms in a polynomial that need to be factored, factor by grouping. Step 1: Group the first two terms together and the second two terms together. Step 2: Factor out the GCF of each grouping. St