 # 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