Properties & Attributes of Functions - Reporting Category 2
Foundations for functions. The student uses the properties and attributes of functions. The student understands how algebra can be used to express generalizations and recognizes and uses the power of symbols to represent situations. The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations.
(A.2) Foundations for functions. The student uses the properties and attributes of functions. The student is expected to
(A) identify and sketch the general forms of linear (y = x) and quadratic (y = x2) parent functions; Supporting Standard
- Slope-intercept form: graph an equation (Algebra 1 - S.5)
- Standard form: graph an equation (Algebra 1 - S.12)
- Point-slope form: graph an equation (Algebra 1 - S.15)
- Identify linear, quadratic, and exponential functions from graphs (Algebra 1 - CC.1)
(B) identify mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete; Readiness Standard
- Domain and range of relations (Algebra 1 - Q.2)
- Domain and range of absolute value functions (Algebra 1 - DD.2)
- Domain and range of radical functions (Algebra 1 - FF.2)
(C) interpret situations in terms of given graphs or create situations that fit given graphs; and Supporting Standard
(D) collect and organize data, make and interpret scatterplots (including recognizing positive, negative, or no correlation for data approximating linear situations), and model, predict, and make decisions and critical judgments in problem situations. Readiness Standard
- Create bar graphs, line graphs, and histograms (Algebra 1 - N.2)
- Interpret a scatter plot (Algebra 1 - N.6)
- Scatter plots: line of best fit (Algebra 1 - N.7)
(A.3) Foundations for functions. The student understands how algebra can be used to express generalizations and recognizes and uses the power of symbols to represent situations. The student is expected to
(A) use symbols to represent unknowns and variables; and Supporting Standard
(B) look for patterns and represent generalizations algebraically. Supporting Standard
- Write variable expressions for arithmetic sequences (Algebra 1 - P.5)
- Write variable expressions for geometric sequences (Algebra 1 - P.6)
- Write a function rule: word problems (Algebra 1 - Q.10)
- Write a rule for a function table (Algebra 1 - Q.12)
(A.4) Foundations for functions. The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations. The student is expected to
(A) find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations; Readiness Standard
- Does x satisfy the equation? (Algebra 1 - I.4)
- Find solutions from a replacement set (Algebra 1 - I.5)
- Solve equations using order of operations (Algebra 1 - I.6)
- Model and solve equations using algebra tiles (Algebra 1 - J.1)
- Write and solve equations that represent diagrams (Algebra 1 - J.2)
- Solve one-step linear equations (Algebra 1 - J.3)
- Solve two-step linear equations (Algebra 1 - J.4)
- Solve advanced linear equations (Algebra 1 - J.5)
- Solve equations with variables on both sides (Algebra 1 - J.6)
- Solve linear equations: word problems (Algebra 1 - J.8)
- Solve linear equations: mixed review (Algebra 1 - J.9)
- Solve one-step linear inequalities: addition and subtraction (Algebra 1 - K.4)
- Solve one-step linear inequalities: multiplication and division (Algebra 1 - K.5)
- Solve one-step linear inequalities (Algebra 1 - K.6)
- Solve two-step linear inequalities (Algebra 1 - K.8)
- Solve advanced linear inequalities (Algebra 1 - K.10)
- Linear equations: solve for y (Algebra 1 - S.8)
- Linear function word problems (Algebra 1 - S.9)
- Polynomial vocabulary (Algebra 1 - Z.1)
- Model polynomials with algebra tiles (Algebra 1 - Z.2)
- Add and subtract polynomials using algebra tiles (Algebra 1 - Z.3)
- Add and subtract polynomials (Algebra 1 - Z.4)
- Add polynomials to find perimeter (Algebra 1 - Z.5)
- Multiply a polynomial by a monomial (Algebra 1 - Z.6)
- Multiply two polynomials using algebra tiles (Algebra 1 - Z.7)
- Multiply two binomials (Algebra 1 - Z.8)
- Multiply two binomials: special cases (Algebra 1 - Z.9)
- Multiply polynomials (Algebra 1 - Z.10)
- GCF of monomials (Algebra 1 - AA.1)
- Factor out a monomial (Algebra 1 - AA.2)
- Factor quadratics with leading coefficient 1 (Algebra 1 - AA.3)
- Factor quadratics with other leading coefficients (Algebra 1 - AA.4)
- Factor quadratics: special cases (Algebra 1 - AA.5)
- Factor by grouping (Algebra 1 - AA.6)
- Factor polynomials (Algebra 1 - AA.7)
(B) use the commutative, associative, and distributive properties to simplify algebraic expressions; and Supporting Standard (C) connect equation notation with function notation, such as y = x + 1 and f (x) = x + 1. Supporting Standard
- Properties of addition and multiplication (Algebra 1 - H.1)
- Distributive property (Algebra 1 - H.2)
- Simplify variable expressions using properties (Algebra 1 - H.3)
- Simplify variable expressions involving like terms and the distributive property (Algebra 1 - I.2)
- Simplify radical expressions using the distributive property (Algebra 1 - EE.5)
- Simplify radical expressions: mixed review (Algebra 1 - EE.6)
(C) connect equation notation with function notation, such as y = x + 1 and f (x) = x + 1. Supporting Standard