Math 104 Unit 1 Outline

Unit 1: Linear Functions

 

**Videos for nearly all these topics can be found by searching at: https://www.khanacademy.org/math.

 

1.0  Algebra Toolbox

  • What do inequality notation and interval notation represent?  How are they related?
  • How do you plot points on the Cartesian coordinate system?
  • What is a polynomial?  How do you determine the degree of a polynomial?
  • How do you simplify an algebraic expression?
  • Words to be familiar with: term, variable, coefficient, constant, leading coefficient, degree.

 

1.1  Functions and Models

  • What is the definition of a function?
  • What is function notation?
  • How do you evaluate a function?
  • What are the domain and range of a function?  How are these found?

 

1.2  Graphs of Functions

  • How do you graph equations with the point-plotting method?
  • How do you graph equations with graphing calculators?
  • When is a graph considered a “complete graph”?
  • How do we align inputs and scale outputs to model data?

 

1.3  Linear Functions

  • What is a linear function?
  • How do you find the intercepts of the graph of a linear function?
  • How do you find the slope of a linear function?
  • How do you graph a linear function?
  • How is the rate of change of a function related to its slope?
  • How is marginal profit related to a profit function?

 

1.4  Equations of Lines

  • What is the slope-intercept form of a linear equation?
  • What is the point-slope form of a linear equation?
  • What do the equations of horizontal and vertical lines look like?
  • How do you find the average rate of change for a function?

 

2.1  Algebraic and Graphical Solution of Linear Equations

  • How do you solve linear equations algebraically?
  • How do you solve linear equations graphically?

 

2.2  Modeling Linear Functions

  • What are the first differences of data outputs?  How can they be used to determine if data can be modeled with a linear function?
  • What is the difference between a discrete function and a continuous function?
  • How do you perform linear regression to find the best-fit line for a set of data?
  • How do you find the sum of squared errors and the average error for a model?
  • What is the difference between interpolation and extrapolation?

 

2.3  Systems of Linear Equations in Two Variables

  • What is the graphical method for solving a system of equations?
  • What is the substitution method for solving a system of equations?
  • What is the elimination method for solving a system of equations?

 

7.1  Systems of Linear Equations in Three Variables

  • How do you solve a system of three equations with three variables?

 

7.2  Matrix Solution of Systems of Linear Equations

  • How can you use a matrix and your calculator to solve a system of equations?

 

Review for Test 1

 

TEST 1