Algebra 2 A Final Review 2015-2016

Vocabulary Domain: The set of first coordinates or x-coordinates Range: The set of second coordinates or y-coordinates Function: A relation in which each element of the domain is paired with exactly one element of the range.

Vocabulary One-to-one function: Each element of the domain pairs to exactly one UNIQUE element of the range. Onto function: Each element of the range corresponds to an element of the domain.

Vocabulary Discrete Relation: A relation in which the domain is a set of individual points. Continuous Relation: Domain of a relation has an infinite number of elements, can be graphed with a smooth curve.

Vocabulary Independent Variable: The domain of a function, usually x. Dependent Variable: The other variable involved with the function. It depends on the domain.

Example #1 { (2, -2), (-1, -1), (-2, 0), (-1, 1), (2, 2)} Domain: Range: Function: Yes or No One-to-one: Yes or No Onto: Yes or No

Example #2 { (-3, 0), (-2, 2), (-1, 6), (0, 4), (1, 6), ( , 8)} { (-3, 0), (-2, 2), (-1, 6), (0, 4), (1, 6), ( , 8)} Domain: Range: Function: Yes or No One-to-one: Yes or No Onto: Yes or No

Function Notation Equation: y = 5x – 1 Function Notation: F(x) = 5x – 1 Using function notation solve the following if f(x) = 2x2 -7 and g(x) = 2(x+5 ) +4x 3. f(2) = 4. g(0) =   5. f(3b) = 6. g(-2) =

Characteristics of a Linear Relation Only operations are +, -, and multiplication of a variable by a constant (ex. 6X ) Variables may not be multiplied together Variables may not appear in the denominator The variables only exponent is 1. The graph is always a line. Can be written in the form y = mx + b or f(x) = mx + b

Examples Determine which things are lines and which are not by writing yes or no. 1. y = 5x + 8 2. 2x +5y +8 = 12 3. 2x3 – y = 8 4. x/2 + 9 = y 5. 5xy = 10 6. 5/y + 6x = 10

Standard Form AX + BY = C Write each linear equation in standard form then identify A, B, and C. 7. 4y + 3x = 9 8. -2x = -7y + 12 9. y = 4x + 8 10. 7x -2y = 3

Writing Equations of Lines Slope Formula y2-y1=x2 –x1 Standard Form Ax + By = C Slope-Intercept Form y = mx +b Point-Slope Form y-y1= m(x-x1)

Parallel and Perpendicular Parallel lines have the same slope. Perpendicular lines have opposite reciprocal slopes.

1. Slope of -1, passes through (-7, -4) Step 1 : Which formula do you use ______________________________ (Write the name here) Step 2.: Write out the formula ___________________________. Step 3: Plug in values: ________________________________________ Step 4: Simplify and get y by itself. Circle answer.

2. Slope of ½ , passes through (4, -8) Step 1 : Which formula do you use ______________________________ (Write the name here) Step 2.: Write out the formula ___________________________. Step 3: Plug in values: ________________________________________ Step 4: Simplify and get y by itself. Circle answer.

3. Passes through (-2, 4) and (0,8) Step 1 : Which formula do you use ______________________________ (Write the name here) Step 2.: Write out the formula ___________________________. Step 3: Find the slope:   Step 4: Plug in values: ________________________________________ Step 5: Simplify and get y by itself. Circle answer.

4. Passes through (3,5) and (-1, 5) Step 1 : Which formula do you use ______________________________ (Write the name here) Step 2.: Write out the formula ___________________________. Step 3: Find the slope:   Step 4: Plug in values: ________________________________________ Step 5: Simplify and get y by itself. Circle answer.

Passes through (7,5), parallel to y=2x -3 Step 1 : What do you know about parallel lines and their slopes: ____________________________ Step 2: Which formula do you use ______________________________ (Write the name here) Step 3.: Write out the formula ___________________________. Step 4: Find the slope: Step 5: Plug in values: ________________________________________ Step 6: Simplify and get y by itself. Circle answer.

6. Passes through (-1, 7), perpendicular to y = ½ x -8 Step 1 : What do you know about parallel lines and their slopes: ____________________________ Step 2: Which formula do you use ______________________________ (Write the name here) Step 3.: Write out the formula ___________________________. Step 4: Find the slope: Step 5: Plug in values: ________________________________________ Step 6: Simplify and get y by itself. Circle answer.

7. Drew paid a $175 fee when he adopted a puppy 7. Drew paid a $175 fee when he adopted a puppy. The average monthly cost of feeding and caring for the puppy is $30. Write and equation that represents the total cost of adopting and caring for the puppy for x months. b. How much will you pay for the puppy after having him 8 months.

1. y = ¼ x – 3 2. 2x = 3y - 9

Solving Systems of Equations using Substitution Steps: 1. Solve one equation for one variable (y= ; x= ; a=) 2. Substitute the expression from step one into the other equation. 3. Simplify and solve the equation. 4. Substitute back into either original equation to find the value of the other variable. 5. Check the solution in both equations of the system.

Solve these systems of equations using substitution. 1.   Y = 2x -10 Y = -4x + 8 2. X +5y = 3 3x -2y = -8

3-2: Solving Systems of Equations using Elimination Steps: 1. Place both equations in Standard Form, Ax + By = C. 2. Determine which variable to eliminate with Addition or Subtraction. 3. Solve for the variable left. 4. Go back and use the found variable in step 3 to find second variable. 5. Check the solution in both equations of the system.

Solve these systems of Equations using Elimination. 1. 4x – 3y = 29 4x + 3y = 35   2. -6w -8z = -44 3w + 6z = 36

Special Cases   No Solution  Parallel Lines A ≠B   INCONSISTENT Infinitely Many Solutions  Same Lines A = A  CONSISTENT & DEPENDENT

Solve using Either Substitution or Elimination. 1. 5a + 15b = -24 -2a -6b = 28   2. 9y + 3x = 18 -3y –x = -6

Set-up but DO NOT SOLVE 1. Peni bought a basketball and a volleyball that cost a total of $67. The price of the basketball b is $4 more than twice the cost of the volleyball v. How much does each ball cost? 2. A caterer bought several pounds of chicken salad and several pounds of tuna salad. The chicken salad costs $9 per pound, and the tuna salad costs $6 per pound. He bought a total of 14 pounds of salad and paid a total of $111. How many pounds of each did he buy?

For any two real numbers, a and b, exactly one of the following is true. A [ ]B A[ ]B A[ ]B ADDITION and SUBTRACTION PROPERTY OF INEQUALITY If a > b Then a + c [ ] b + c and a – c [ ] b - c If a < b MULTIPLICATION and DIVISION PROPERTY OF INEQUALITY Where C is POSITIVE (+) Then ac [ ] bc and a/c [ ] b/c Where C is NEGATIVE (-)

Simplify the following Inequalities 2. 4 – 7x > 2(x +3) 3. –p -13 ≤ 3(5+ 4p) -2

y ≥ 2x + 1 Step 1 : Write in slope intercept form y [ ] mx + b Step 2: Graph the line. IF <, > - ------- DASHED, IF ≤, ≥ _____________ SOLID Step 3: Pick a test point and plug in. Shade the TRUE side

X – 3y < 6 Step 1 : Write in slope intercept form y [ ] mx + b Step 2: Graph the line. IF <, > - ------- DASHED, IF ≤, ≥ _____________ SOLID Step 3: Pick a test point and plug in. Shade the TRUE side

Constructed Responses

About the FINAL: *Your final for Algebra 2 will be held on ____________________________ at __________________. *There are __________ Multiple Choice Questions and _____________ Short Answer Questions. *You may use one handwritten 3x5 notecard on the final. Calculators may also be used on the final. *This packet will be due before you take your final NOT after. *Students need to follow all Destiny High School rules in order to receive their final including Dress Code. Electronic devices will not be allowed in testing room. Students who violate the rules or are found disrupting other students during the final will have their test confiscated and asked to leave.