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Worksheet/Answer keyFunctions

MD.MA.AI. Algebra I

Unit 1: Relationships between Quantities and Reasoning with Equations

HSA-SSE.A. Interpret the structure of expressions.

A.SSE.1a. Interpret expressions that represent a quantity in terms of its context – Interpret parts of an expression, such as terms, factors, and coefficients.

A.SSE.1a.1. Ability to make connections between symbolic representations and proper mathematics vocabulary.

A.SSE.1b. Interpret expressions that represent a quantity in terms of its context – Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)^n as the product of P and a factor not depending on P.

A.SSE.1b.1. Ability to interpret and apply rules for order of operations.

Unit 2: Linear and Exponential Relationships

HSF-IF.A. Understand the concept of a function and use function notation.

F.IF.1. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

F.IF.1.1. Ability to determine if a relation is a function.

HSF-LE.A. Construct and compare linear, quadratic, and exponential models and solve problems.

F.LE.1a. Distinguish between situations that can be modeled with linear functions and with exponential functions – Prove that linear functions grow by equal differences over equal intervals; and that exponential functions grow by equal factors over equal intervals.

F.LE.1a.1. See the skills and knowledge that are stated in the Standard.

Unit 5: Quadratic Functions and Modeling

HSF-IF.B. Interpret functions that arise in applications in terms of a context.

F.IF.4. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

F.IF.4.2. Ability to connect experiences with linear and exponential functions from Unit 2 of this course to quadratic, square root, cube root, absolute value, step and piecewise defined models.

F.IF.5. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.

F.IF.5.3. Ability to connect experiences with linear and exponential functions from Unit 2 of this course to quadratic, square root, cube root, absolute value, step and piecewise defined models.

MD.MA.AII. Algebra II

Unit 1: Polynomial, Rational, and Radical Relationships

HSA-SSE.B. Write expressions in equivalent forms to solve problems.

A.SSE.3c. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression – Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15^t can be rewritten as (1.15^1/12)^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.

A.SSE.3c.2. Ability to connect experience with properties of exponents from Unit 4 of Algebra I to more complex expressions

HSG-GPE.A. Translate between the geometric description and the equation for a conic section.

G.GPE.2. Derive the equation of a parabola given a focus and directrix.

G.GPE.2.2. Ability to connect the algebraic and geometric definitions of a parabola.

Unit 3: Modeling with Functions

HSF-BF.A. Build a function that models a relationship between two quantities.

F.BF.1a. Write a function that describes a relationship between two quantities – Determine an explicit expression, a recursive process, or steps for calculation from a context.

F.BF.1a.1. Ability to connect experience with linear and exponential functions from Algebra I Unit 2 to quadratic functions.

HSF-LE.B. Interpret expressions for functions in terms of the situation they model.

F.LE.5. Interpret the parameters in a linear or exponential function in terms of a context.

F.LE.5.2. Ability to identify the initial amount present in an exponential model (f(0) = b^0+k = 1+k).

F.LE.5.3. Ability to interpret the rate of increase/decrease in an exponential model.

Standards