### NQ: Number and Quantity

#### 1.1: Explore and illustrate the characteristics and operations connecting sequences and series

NQ.1: Express sequences and series using recursive and explicit formulas.

NQ.2: Evaluate and apply formulas for arithmetic and geometric sequences and series.

### A: Algebra

#### 2.1: Analyze and manipulate functions

A.8: Determine characteristics of graphs of parent functions (domain/range, increasing/decreasing intervals, intercepts, symmetry, end behavior, and asymptotic behavior).

#### 2.2: Use polynomial identities to solve problems

A.10: Prove polynomial identities and use them to describe numerical relationships.

A.12: Know and apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle.

A.15: Determine asymptotes and holes of rational functions, explain how each was found, and relate these behaviors to continuity.

#### 2.3: Perform operations on expressions, equations, inequalities and polynomials

A.18: Find the composite of two given functions and find the inverse of a given function. Extend this concept to discuss the identity function f(x) = x.

A.21: Find the zeros of polynomial functions by synthetic division and the Factor Theorem.

A.22: Graph and solve quadratic inequalities.

### F: Functions

#### 3.1: Analyze functions using different representations

F.24: Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

#### 3.2: Build a function that models a relationship between two quantities

F.25: Compose functions.

#### 3.3: Build new functions from existing functions

F.26: Verify by composition that one function is the inverse of another.

F.27: Read values of an inverse function from a graph or a table, given that the function has an inverse.

F.28: Produce an invertible function from a non-invertible function by restricting the domain.

F.29: Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

#### 3.4: Extend the domain of trigonometric functions using the unit circle

F.30: Use special triangles to determine geometrically the values of sine, cosine, tangent for pi/3, pi/4 and pi/6, and use the unit circle to express the values of sine, cosine, and tangent for pi – x, pi + x, and 2pi – x in terms of their values for x, where x is any real number.

F.31: Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

#### 3.5: Model periodic phenomena with trigonometric functions

F.32: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

#### 3.6: Prove and apply trigonometric identities

F.35: Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

F.36: Prove the Pythagorean identity sin²(theta) + cos²(theta) = 1 and use it to find sin(theta), cos(theta), or tan(theta) given sin(theta), cos(theta), or tan(theta) and the quadrant of the angle.

### G: Geometry

#### 4.1: Recognize, sketch, and transform graphs of functions

G.37: Graph piecewise defined functions and determine continuity or discontinuities.

G.38: Describe the attributes of graphs and the general equations of parent functions (linear, quadratic, cubic, absolute value, rational, exponential, logarithmic, square root, cube root, and greatest integer).

G.39: Explain the effects of changing the parameters in transformations of functions.

G.40: Predict the shapes of graphs of exponential, logarithmic, rational, and piece-wise functions, and verify the prediction with and without technology.

### SP: Statistics and Probability

#### 5.1: Explore and apply fundamental principles of probability.

SP.45: Analyze expressions in summation and factorial notation to solve problems.

Correlation last revised: 9/15/2020

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.