Algebra I & Concepts Ch. 1 Notes

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) Operation Verbal Phrases Addition Subtraction Multiplication Division

Section 1-1 Ex2) Write the algebraic expression for the verbal expression A number t more than 6 10 less than the product of 7 and f Two thirds of v

Section 1-2: Order of Operations Parenthesis and brackets Exponents Multiplication & Division Addition &Subtraction

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 1-3: Properties of Numbers Property Words Symbols Examples Reflexive Property Any quantity is equal to itself Symmetric Property If one quantity equals a second quantity, then the second quantity equals the first Transitive Property If one quantity equals a second quantity and the second equals a third, the the first and third are equal Substitution Property A quantity may be substituted for its equal in any expression

Section 1-3: Addition and Multiplication Properties Property Words Symbols Example Additive Identity For any number a, the sum of a and 0 is a Additive Inverse A number and its opposite are additive inverses of each other Property Words Symbols Example Multiplicative Identity For any number a, the product of a and 1 is a Multiplicative Property of Zero For any number a, the product of a and 0 is 0. Multiplicative Inverse (Reciprocal) The product of any number and its reciprocal is 1

Section 1-3 Ex1) Evaluate the expressions a) b) Commutative Property (add. & mult.)- Associative Property (add. & mult.)-

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

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

Section 1-5: Equations Equations vs. Expressions: Solving and the Solution: Ex1) Find the solution set of the equation 2x + 5 = 13 if the replacement set is {2, 3, 4, 5, 6}

Section 1-5 Ex2) Apply Order of Operations to solve for the variable a) b) One solution, no solutions, all real numbers

Section 1-5 Ex3) Determine if the equation has one, no, or all real solutions a) b)

Section 1-5 Ex4) Determine if the given number is a solution to the equation 12 + y = 26; 14 b) 2t – 10 = 4; 3 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 Domain Range X Y

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

Section 1-6 Independent Variable – Dependent Variable – Ex2) Identify the dependent and independent variables The dance committee is selling tickets to the Fall Ball. The more tickets they sell, the more money they can spend on decorations. 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 The dance committee is selling tickets to the Fall Ball. The more tickets they sell, the more money they can spend on decorations. 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 Dom. Range b) -2 -3 0 6 3 9 c) {(2,1), (3,-2), (3,1), (2,-1)} 4 Domain 1 3 5 Range 4 2 -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: Identify as linear or nonlinear Estimate the intercepts Find symmetry (if possible)