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Henrico County Public Schools, Virginia
Algebra and Functions

Data Analysis

SOL Review Materials
The student will investigate and analyze function (linear, quadratic, exponential, and logarithmic) families and their characteristics. Key concepts include:
a)   continuity;
b)   local and absolute maxima and minima;
c)   domain and range;
d)   zeros;
e)   intercepts;
f)   intervals in which the function is increasing/decreasing;
g)   end behaviors; and  
h)   asymptotes.
Essential Knowledge and Skills 
  • Identify the domain and range for a relation, given a set of ordered pairs, a table, or a graph.
  • For each x in the domain of f, find f(x).
  • Identify the zeros of the function algebraically and confirm them, using the graphing calculator.
  • Identify the domain, range, zeros, and intercepts of a function presented algebraically or graphically.
  • Recognize restricted/discontinuous domains and ranges.
  • Recognize graphs of parent functions for linear, quadratic, exponential and logarithmic functions.
  • Identify x-intercepts (zeros), y-intercepts, symmetry, asymptotes, intervals for which the function is increasing or decreasing, points of discontinuity, end behavior, and maximum and minimum points, given a graph of a function.
  • Describe continuity of a function on its domain or at a point.
  • Express intervals using correct interval notation and/or a compound inequality.
Essential Understandings
  • The domain of a function consists of the first coordinates of the ordered pairs that are elements of a function.   Each element in the domain is an input into the independent variable of the function.
  • The range of a function consists of the second coordinates of the ordered pairs that are elements of a function.  Each element in the range is an output in the dependent variable of a function.
  • For each x in the domain of f, x is a member of the input of the function f, f(x) is a member of the output of f, and the ordered pair [x, f(x)] is a member of f.
  • A value x in the domain of f is an x-intercept or a zero of a function f if and only if f(x) = 0.
  • Functions describe the relationship between two variables where each input is paired to a unique output.
  • Functions are used to model real-world phenomena.
  • A function is increasing on an interval if its graph, as read from left to right, is rising in that interval.
  • A function is decreasing on an interval if its graph, as read from left to right, is going down in that interval.
  • Exponential and logarithmic functions are either strictly increasing or strictly decreasing.
  • A function is continuous on an interval if the function is defined for every value in the interval and there are no breaks in the graph.  A continuous function can be drawn without lifting the pencil.
  • A turning point is a point on a continuous interval where the graph changes from increasing to decreasing or from decreasing to increasing.
  • A function, f, has a local maximum in some interval at x = a if f(a) is the largest value of f in that interval.
  • A function, f, has a local minimum in some interval at x = a if f(a) is the smallest value of f in that interval.
  • Asymptotes can be used to describe local behavior and end behavior of graphs.  They are lines or other curves that approximate the graphical behavior of a function.
  • The following statements are equivalent:
    • k is a zero of the polynomial function f;
    • k is a solution of the polynomial equation f(x) = 0;
    • k is an x-intercept for the graph of the polynomial; and
    • (x - k) is a factor of the polynomial.
  • Continuous and discontinuous functions can be identified by their equations or graphs.  The end behavior of a function refers to the graphical behavior of a function as x goes to positive and negative infinity.
Vertical Articulation
  1. SOL 8.17 - Identify domain, range, independent, dependent variable.
  2. SOL A.7 - investigate/analyze function (linear/quad)families and characteristics(alg/graph) ‐ a) determine if a relation is function; b) domain/range; c)zeros; d) x‐ and y‐ intercepts; e) find values offunct for elementsin domain; f) make
    connections between/among mult representations of functions (concrete/verbal/ numeric/graphic/algebraic).
  3. SOL AII.7 - investigate/analyze functions (alg/graph) a) domain/range; b) zeros; c) x‐ and y‐intercepts; d) intervals inc/dec; e) asymptotes; f) end behavior; g)inverse of a function; h) composition of multiple functions.
Instructional Materials
Frederick County Resources
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Skills
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Common Core Standards