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.
Homework: Page 9 #11, 13, 19, 25, 27, 31, 35-41 odd
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?
Homework: Pages 20-26 #7, 11-19 odd, 27, 51, 53, 59
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?
Homework: Pages 37-40 #1, 11, 19, 35, 37, 39, 49
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?
Homework: Pages 54-58 #3, 7, 19, 25, 27, 33, 37, 49, 55, 59
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?
Homework: Pages 70-75 #3, 5, 9, 11, 27, 39, 49, 67
2.1 Algebraic and Graphical Solution of Linear Equations
- How do you solve linear equations algebraically?
- How do you solve linear equations graphically?
Homework: Pages 101-104 #9, 11, 21, 37, 47, 59, 63, 67, 81
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?
Homework: Pages 118-123 #23, 33, 35, 41
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?
Homework: Pages 135-137 #7, 11, 21, 23, 29, 31, 35, 45
7.1 Systems of Linear Equations in Three Variables
- How do you solve a system of three equations with three variables?
Homework: Pages 518-520 #11, 13, 15, 27, 33
7.2 Matrix Solution of Systems of Linear Equations
- How can you use a matrix and your calculator to solve a system of equations?
Homework: Pages 531-532 #15, 17, 19, 33
Review for Test 1