Functions and Their Graphs

1-1              Graphs of Equations

  1. Sketch graphs of equations

  2. Find x and y intercepts of graphs

  3. Use symmetry to sketch graphs of equations

  4. Find equations and sketch graphs of circles

  5. Use graphs of equations in real life situations

 1-2              Linear Equations in two variables

  1. Use slope to graph linear equations in two variables

  2. Find slopes of lines

  3. Write linear equations in two variables

  4. Use slope to identify parallel and perpendicular lines

  5. Use linear equations in two variables to model real life situations

1-3              Functions

  1. Decide whether relations between two variables are functions

  2. Use functions notation and evaluate functions

  3. Find the domain of functions

  4. Use functions to model and solve real life problems

1-4              Analyzing Graphs of Functions

  1. Use the vertical line test for functions

  2. Find the zeros of functions

  3. Determine intervals on which functions are increasing, decreasing or constant

  4. Identify and graph linear functions

  5. Identify and graph step functions and other piece-wise defined functions

  6. Identify even and odd functions

1-5              Shifting, Reflecting and Stretching Graphs

  1. Recognize graphs of common functions

  2. Use vertical and horizontal shifts to sketch graphs of functions

  3.  Use reflections to sketch graphs of functions

  4.  Use nonrigid transformations to sketch graphs of functions

1-6              Combinations of functions

  1. Add, subtract, multiply and divide functions

  2. Find compositions of one function with another

  3. Use combinations of functions to model and solve real life problems

1-7              Inverse Functions

  1. Find inverse functions informally and verify that two functions are inverses of each other.

  2. Use graphs of functions to decide whether functions have inverses

  3. Find inverse functions algebraically

1-8              Mathematical Modeling

  1. Write mathematical models for direct variation

  2. Write mathematical models for inverse variation

  3. Write mathematical models for joint variation