Algebra I Concepts Ch. 1 Notes Expressions, Equations, and Functions.
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Transcript of Algebra I Concepts Ch. 1 Notes Expressions, Equations, and Functions.
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Algebra I Concepts
Ch. 1 NotesExpressions, Equations, and
Functions
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Section 1-1: Variables and Expressions
Algebraic Expression-
Variable-
Term-
Exponent-
Base-
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Section 1-1
Ex1) Write the verbal expression for each algebraic expressionsa) b)
Operation Verbal Phrases
Addition
Subtraction
Multiplication
Division
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Section 1-1
Ex2) Write the algebraic expression for the verbal expression
a) A number t more than 6
b) 10 less than the product of 7 and f
c) Two thirds of v
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Section 1-2: Order of Operations
Parenthesis and brackets
Exponents
Multiplication & Division
Addition &Subtraction
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Section 1-2
Ex1) Evaluate the expression
Ex2) Evaluate each expressiona) b)
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Section 1-2
c) d)
Ex3) Evaluate when x = 4, y = 5, z = 3a)
b)
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Section 1-4: The Distributive Property
Distributive Property –
Ex1) Rewrite using the Distributive Propertya) 7(3w – 5) b)
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Section 1-4: The Distributive Property
Distributive Property – For any numbers a, b, and c: a(b + c) = ab + acEx) 2(3 + 4) = (2 x 3) + (2 x 4)
Ex1) Rewrite using the Distributive Propertya) 7(3w – 5) b)
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Section 1-4
Like Terms –
Simplest Form –
Ex2) Simplifya) 17u + 25u b)
c) d)
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Section 1-4
Like Terms – terms that have the same variable part
Simplest Form – contains no parenthesis or like terms
Ex2) Simplifya) 17u + 25u b)
c) d)
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Section 1-6: RelationsCoordinate Plane
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Section 1-6: Plotting Points
Plot and label the following points on the graph, and identify the location of the point (I, II, III, IV, x-axis, y-axis, origin).A(3, 5)B(-2, 4)C(-1, -7)D(5, -8)E(3, 0)F(0, -6)
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Section 1-6
Ordered Pair-
X-coordinate-
Y-coordinate
Relation
Domain-
Range-
Mapping
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Section 1-6: Vocabulary
Ordered Pair- set of numbers of coordinates written in the form (x, y)
X-coordinate- the horizontal placement of the point
Y-coordinate- the vertical placement of the point
Relation- a set of ordered pairs
Domain- first number in the ordered pair (typically x), also called the input
Range- second number in the ordered pair (typically y), also called the output
Mapping- shows how each element of the domain is paired with an element in the range
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Section 1-6: All the Same!
Ordered Pairs: (1, 2), (-2, 4), (0, 3)Table
Graph
MappingDomainRange
X Y
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Section 1-6
Ex1) Express [(2,5), (-2,3), (5,-2), (-1,-2)] as a table, a graph, and mappingTABLE GRAPH
MAPPING
Determine the domain and range!
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Section 1-6Independent Variable –
Dependent Variable –
Ex2) Identify the dependent and independent variablesa) The dance committee is selling tickets to the Fall Ball. The more
tickets they sell, the more money they can spend on decorations.
b) Generally, the average price of movie tickets had increased over time.
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Section 1-6Independent Variable – the variable that determines the output
Dependent Variable – the variable whose value is dependent on the independent variable
Ex2) Identify the dependent and independent variablesa) The dance committee is selling tickets to the Fall Ball. The more tickets
they sell, the more money they can spend on decorations.
b) Generally, the average price of movie tickets had increased over time.
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Section 1-7: Functions
Function – a relationship between input and output. For each input there is one outputEx1) Determine if the relationships are functionsa) Dom.Range b)-2 -30 63 9 c) {(2,1), (3,-2), (3,1), (2,-1)}4
Domain 1 3 5 1
Range 4 2 4 -4
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Section 1-7Discrete Function –
Continuous Function –
Vertical Line Test -
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Section 1-7
Ex2) Determine if whether -3x + y = 8 is a function
Function Notation -
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Section 1-8: Interpreting Graphs of Functions
Intercepts –
Y – intercept –
X – intercept –
Line of Symmetry –
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Section 1-8: Interpreting Graphs of Functions
Intercepts – the points on a graph that intersect with an axis
Y – intercept – the point where a graph crosses the y-axis
X – intercept – the point where a graph crosses the x-axis
Line of Symmetry – a vertical line the cuts a graph in half
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Section 1-8
Ex1) For each graph:a) Identify as linear or nonlinearb) Estimate the interceptsc) Find symmetry (if possible)