New York flagNew York: AI-F Math Standards

18 standards · 3 domains

FUNCTIONS - BUILDING FUNCTIONS

  • AI-F.BF.1.a Determine a function from context. Define a sequence explicitly or steps for calculation from a context. (Shared standard with Algebra II)
  • AI-F.BF.3a Using f(x) + k, k f(x), and f(x + k): i) identify the effect on the graph when replacing f(x) by f(x) + k, k f(x), 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. (Shared standard with Algebra II)

FUNCTIONS - INTERPRETING FUNCTIONS

  • AI-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).
  • AI-F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
  • AI-F.IF.3 Recognize that a sequence is a function whose domain is a subset of the integers. (Shared standard with Algebra II)
  • AI-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 II)
  • AI-F.IF.5 Determine the domain of a function from its graph and, where applicable, identify the appropriate domain for a function in context.
  • AI-F.IF.6 Calculate and interpret the average rate of change of a function over a specified interval. (Shared standard with Algebra II)
  • AI-F.IF.7.a Graph linear, quadratic, and exponential functions and show key features.
  • AI-F.IF.7.b Graph square root, and piecewise-defined functions, including step functions and absolute value functions and show key features.
  • AI-F.IF.8.a For a quadratic function, use an algebraic process to find zeros, maxima, minima, and symmetry of the graph, and interpret these in terms of context.
  • AI-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 II)

FUNCTIONS - LINEAR, QUADRATIC, AND EXPONENTIAL MODELS

  • AI-F.LE.1.a Justify that a function is linear because it grows by equal differences over equal intervals, and that a function is exponential because it grows by equal factors over equal intervals.
  • AI-F.LE.1.b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another, and therefore can be modeled linearly.
  • AI-F.LE.1.c Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another, and therefore can be modeled exponentially.
  • AI-F.LE.2 Construct a linear or exponential function symbolically given: i) a graph; ii) a description of the relationship; iii) two input-output pairs (include reading these from a table). (Shared standard with Algebra II)
  • AI-F.LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
  • AI-F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context. (Shared standard with Algebra II)