Algebra I (MAT111) Syllabus

- (F-IF) Domain

Interpreting Functions

Understand the concept of a function and use function notation

  • MAT-HS.F-IF.01 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).
  • MAT-HS.F-IF.02 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
  • MAT-HS.F-IF.03 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

Interpret functions that arise in applications in terms of the context

  • MAT-HS.F-IF.04 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.
  • MAT-HS.F-IF.05 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
  • MAT-HS.F-IF.06 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Analyze functions using different representations

  • MAT-HS.F-IF.07 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
    • MAT-HS.F-IF.07.a Graph linear and quadratic functions and show intercepts, maxima, and minima.
    • MAT-HS.F-IF.07.b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
    • MAT-HS.F-IF.07.c Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
    • MAT-HS.F-IF.07.d Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
    • MAT-HS.F-IF.07.e.- Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
  • MAT-HS.F-IF.08 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
    • MAT-HS.F-IF.08.a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
    • MAT-HS.F-IF.08.b Use the properties of exponents to interpret expressions for exponential functions.
  • MAT-HS.F-IF.09 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).