Unit 2 Modeling with Functions

When you are finished with the Unit 1 Test:

• Write down in your notes the vocabulary words for Unit 2 using the glossary in the back of your workbook
• Work on 2.1 Warm Up on page 55
• Math is Fun - Absolute Values in Algebra read through this website on the explanation on absolute values
• Absolute Values and Inequalites- Purple Math

2.1 Creating Absolute Value Equations and Inequalities in One Variable

Vocabulary: absolute value, absolute value function, vertex

• Evaluate absolute value functions and graph functions on a coordinate plane
• Solve absolute value equations and inequalities
• Create absolute value inequalities based on real world problems
• YouTube Video on Solving Absolute Value Equations

HW: 2.1 Absolute Value Worksheet

2.7 Reteach on Absolute Value Transformations

Additional Resources: CoolMath - Absolute Values

SEE NOTES BELOW

2.2 Absolute Value and Step Functions

Vocabulary: ceiling function, floor function, greatest integer function, least integer function, step function

• Graph absolute value functions by hand and using the graphing calculator (MATH->NUM->1)abs)
• Graph absolute value functions based on a word problem
• Graph step function by hand and using the graphing calculator (MATH ->NUM -> 5)int)
• Math is Fun - Ceiling and Floor Functions
• Mathbits- Piecewise, Absolute, Step Functions

HW: 2.2 pg 69, 70 Practice B #1-10

2.3 Creating and Graphing Absolute Value Equations and Inequalities in Two Variables

Vocabulary: dependent system, empty set, point(s) of intersection, solution set, system of equations

SOLVING SYSTEMS OF EQUATIONS

• A system of equations is a set of equations with the same unknown (may be the same type of equations or be different types)
• A solution set is the set of ordered pairs that represents all of the solutions to an equation or system of equations
  • Graphically identified as the point(s) of intersection of the graphs
  • Algebraically when the two functions are set equal to each other (ex. f(x) = g(x) )
  • Numerically in a table when both outputs y1 and y2 are equal to each other for a specific x
• 3 Possible Outcomes
  • Solution set written with braces { (x1, y1), (x2, y2)....}
  • No solution, empty set, null set { }, Ø
  • Infinite number of solutions, intersects at every point, “dependent system”

• On graphing calculator, enter each function in y1 and y2, graph so that intersection can be seen or adjust Window dimensions so intersection is visible, 2ND Trace and 5)Intersect and move cursor to one of the points of intersection

SOLVING SYSTEMS OF INEQUALITIES

• Solution is not a set of points but the intersection of partial planes which cannot be written out but solution is shown graphically.
• Greater than is above the graphed line or curve, Less than is below the line or curve
• To show this on the graphing calculator, move to the far left of the “y =” and highlight the “/” this can be changed using the enter key to either a dashed line or the triangle highlighted above for area greater than the graphed function, and triangle highlighted below for the area less than the graphed function

2.4 Piecewise Functions

Vocabulary: piecewise function

2.5 Operating on Functions

Vocabulary: continuous function, discontinuous function, discrete function