110-1     Concept of Function

Students will be able to…

  1. Identify if a relationship is a function and justify with the definition of a function.
  2. Demonstrate proper use of function notation.

Given any of the four representations of a function, (algebraic, table, graph, contextual), students will be able to …

  1. Identify independent and dependent variables.
  2. Identify domain and range using interval or inequality notation.

**for all functions not listed in 110-2

110-2     Families of Functions

Students will be able to identify, solve for, and/or interpret the characteristics of each family of functions as appropriate (linear(L), exponential(E), logarithmic(G), power(P), polynomial(Y), quadratic(Q)):

  1. Intercepts
  2. Rates of Change
  3. Asymptotes
  4. End Behavior
  5. Domain and Range (using interval or inequality notation).
  6. Maximum and Minimum

Given any of the four representations of a function, students will be able to …

  1. Identify the function family
  2. Match to an equivalent representation
  3. Create an equivalent representation

Students will be able to write the equation for

  1. A linear function (from the vertical intercept and a rate OR from two points)
  2. A piecewise function (from a table, graph or context)
  3. An exponential function (from the vertical intercept and a rate, from the vertical intercept and another point,  or from financial information)
  4. A power function  (from context)

Given any of the four representation of a function, students will be able to identify and apply simple transformations:

  1. Horizontal/vertical shifts
  2. Horizontal/vertical axis reflections

110-3     Modeling with technology

Given data, students will be able to …

  1. Identify the most appropriate model based both on technology and the context of the situation and justify reasoning.
  2. Use technology (regression) to find a curve of best fit.

110-4     Algebraic Manipulation

Students will be able to perform the following manipulative skills and interpret the results:

  1. Given input, find output.
  2. Given output, find input.

Students will be able to perform the following manipulative skills with algebraic expressions and equations:

  1. Use the rules of integer and rational exponents to simplify simple expressions.
  2. Rewrite a logarithmic equation into exponential form and vice versa.
  3. Factor simple equations.

110-5     Systems

Given a system of linear equations…

  1. Write equations for the system (in standard or slope-intercept form).
  2. Solve and interpret the results of a system of equations both graphically and algebraically.

Given a system of inequalities…

  1. Write the system of inequalities.
  2. Solve the system graphically.

110-6     Composition and Inverses

  1. Perform a composition of two functions both with specific numbers and with variables.
  2. Find the inverse of a given function using proper inverse function notation.
  3. Given a context and a function such as t-1(4)=20, a student will be able to interpret the equation in context.

110-7     General Mathematical Skills

  1. Explain complex mathematical concepts and procedures using appropriate mathematical terminology.
  2. Organize and update a math portfolio as directed in a portfolio.