New York: AII-F Math Standards
23 standards · 4 domains
FUNCTIONS - BUILDING FUNCTIONS
- AII-F.BF.1.a Determine a function from context. Determine an explicit expression, a recursive process, or steps for calculation from a context. (Shared standard with Algebra I)
- AII-F.BF.1.b Combine standard function types using arithmetic operations.
- AII-F.BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
- AII-F.BF.3b Using f(x) + k, k f(x), f(kx), and f(x + k): i) identify the effect on the graph when replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); ii) find the value of k given the graphs; iii) write a new function using the value of k; and iv) use technology to experiment with cases and explore the effects on the graph. Include recognizing even and odd functions from their graphs. (Shared standard with Algebra I)
- AII-F.BF.4a Find the inverse of a one-to-one function both algebraically and graphically.
- AII-F.BF.5a Understand inverse relationships between exponents and logarithms algebraically and graphically.
- AII-F.BF.6 Represent and evaluate the sum of a finite arithmetic or finite geometric series, using summation (sigma) notation.
- AII-F.BF.7 Explore the derivation of the formulas for finite arithmetic and finite geometric series. Use the formulas to solve problems.
FUNCTIONS - INTERPRETING FUNCTIONS
- AII-F.IF.3 Recognize that a sequence is a function whose domain is a subset of the integers. (Shared standard with Algebra I)
- AII-F.IF.4 For a function that models a relationship between two quantities: i) interpret key features of graphs and tables in terms of the quantities; and ii) sketch graphs showing key features given a verbal description of the relationship. (Shared standard with Algebra I)
- AII-F.IF.6 Calculate and interpret the average rate of change of a function over a specified interval. (Shared standard with Algebra I)
- AII-F.IF.7.c Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
- AII-F.IF.7.e Graph cube root, exponential and logarithmic functions, showing intercepts and end behavior; and trigonometric functions, showing period, midline, and amplitude.
- AII-F.IF.8.b Use the properties of exponents to interpret exponential functions, and classify them as representing exponential growth or decay.
- AII-F.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). (Shared standard with Algebra I)
FUNCTIONS - LINEAR, QUADRATIC, AND EXPONENTIAL MODELS
- AII-F.LE.2 Construct a linear or exponential function symbolically given: i) a graph; ii) a description of the relationship; and iii) two input-output pairs (include reading these from a table). (Shared standard with Algebra I)
- AII-F.LE.4 Use logarithms to solve exponential equations, such as abct = d (where a, b, c, and d are real numbers and b > 0) and evaluate the logarithm using technology.
- AII-F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context. (Shared standard with Algebra I)
FUNCTIONS - TRIGONOMETRIC FUNCTIONS
- AII-F.TF.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
- AII-F.TF.2 Apply concepts of the unit circle in the coordinate plane to calculate the values of the six trigonometric functions given angles in radian measure.
- AII-F.TF.4 Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
- AII-F.TF.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, horizontal shift, and midline.
- AII-F.TF.8 Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1. Find the value of any of the six trigonometric functions given any other trigonometric function value and when necessary find the quadrant of the angle.