Algebra I Concepts Ch. 1 Notes Expressions, Equations, and Functions

Section 1-1: Variables and Expressions Algebraic Expression- Variable- Term- Exponent- Base-

Section 1-1 Ex1) Write the verbal expression for each algebraic expressions a)b) OperationVerbal Phrases Addition Subtraction Multiplication Division

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

Section 1-2: Order of Operations

Section 1-2 Ex1) Evaluate the expression Ex2) Evaluate each expression a)b)

Section 1-2 c)d) Ex3) Evaluate when x = 4, y = 5, z = 3 a)b)

Section 1-4: The Distributive Property Distributive Property – Ex1) Rewrite using the Distributive Property a) 7(3w – 5)b)

Section 1-4: The Distributive Property Distributive Property – For any numbers a, b, and c: a(b + c) = ab + ac Ex) 2(3 + 4) = (2 x 3) + (2 x 4) Ex1) Rewrite using the Distributive Property a) 7(3w – 5)b)

Section 1-4 Like Terms – Simplest Form – Ex2) Simplify a) 17u + 25ub) c) d)

Section 1-4 Like Terms – terms that have the same variable part Simplest Form – contains no parenthesis or like terms Ex2) Simplify a) 17u + 25ub) c) d)

Section 1-6: Relations Coordinate Plane

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)

Section 1-6 Ordered Pair- X-coordinate- Y-coordinate Relation Domain- Range- Mapping

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

Section 1-6: All the Same! Ordered Pairs: (1, 2), (-2, 4), (0, 3) Table Graph Mapping DomainRange XY

Section 1-6 Ex1) Express [(2,5), (-2,3), (5,-2), (-1,-2)] as a table, a graph, and mapping TABLEGRAPHMAPPING Determine the domain and range!

Section 1-6 Independent Variable – Dependent Variable – Ex2) Identify the dependent and independent variables a)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.

Section 1-6 Independent 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 variables a)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.

Section 1-7: Functions Function – a relationship between input and output. For each input there is one output Ex1) Determine if the relationships are functions a)Dom.Rangeb) c) {(2,1), (3,-2), (3,1), (2,-1)} 4 Domain1351 Range424-4

Section 1-7 Discrete Function – Continuous Function – Vertical Line Test -

Section 1-7 Ex2) Determine if whether -3x + y = 8 is a function Function Notation -

Section 1-8: Interpreting Graphs of Functions Intercepts – Y – intercept – X – intercept – Line of Symmetry –

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

Section 1-8 Ex1) For each graph: a)Identify as linear or nonlinear b)Estimate the intercepts c)Find symmetry (if possible)