Name: ________________________________________ Date
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|What you need to know & be able|Things to remember |Problem |Problem |
|to do | | | |
|Recognize a Function |Make sure the same x doesn’t |Function or Not a Function? Why? |Function or Not a Function? Why? |
| |have different y’s |1. (2, 3) (-2, 5) (3, 3) (-2, 5) |2. |
| |In a graph, it should pass the| |3 |
| |vertical line test | |4 |
| | | |3 |
| | | |5 |
| | | | |
| | | |7 |
| | | |-2 |
| | | |-7 |
| | | |-2 |
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|Evaluate Function Notation from|Pick the correct function and |Evaluate questions 3-6 using the following functions: |
|an Equation |plug in for all variables. |[pic] [pic] [pic] |
| | |f(3) = |g(-2) = |
| | | | |
| | |g(3) = |h(-1) = |
|Evaluate Function Notation from|Remember that a table is |Use the following table to answer questions |G(3) = |
|a Table |already a set of inputs and |7-9. | |
| |outputs |X |G(6) = |
| | |2 | |
| | |3 |G(x) = -1, x = |
| | |4 | |
| | |5 | |
| | |6 | |
| | | | |
| | |G(x) | |
| | |-1 | |
| | |-3 | |
| | |-4 | |
| | |-3 | |
| | |-1 | |
| | | | |
| | | | |
|Evaluate Function Notation from|Find the correct coordinate |Use the following graph to answer questions |M(6) = |
|a Graph |pair from the graph. |10-12. | |
| |If you know the y-value, there|Think of the graph below as function M(h) where|M(h) = 2, h = |
| |might be multiple x-values |h is the time in hours and M is her miles from | |
| | |home. |Explain the meaning of #10 and #11. |
| | |[pic] | |
|Find Average Rate of Change |Find y’s for each x. | For -2 < x < 3 | For –1 < x < 2 |
| |Use formula [pic] |f(x) = 3x – 4 |x |
| | | |-1 |
| | | |0 |
| | | |1 |
| | | |2 |
| | | | |
| | | |H(x) |
| | | |5 |
| | | |3.5 |
| | | |2 |
| | | |0.5 |
| | | | |
|Isolate a Variable in a Formula|PEMDAS |Solve for x: y = -5x + 45 |Solve for L: P = 2(L + W) |
| |Backwards, from the ground up!| | |
|Describe the Domain and Range |Continuous functions are |Describe the domain and range of the following. |
|of a Function |CONNECTED and use interval | |
| |notation | |
| |___ < x < ___ | |
| |Discrete functions are NOT | |
| |CONNECTED and use set notation| |
| |{__, __, __, __} | |
| | |(2, 4) (3, -3) (1, 5) (-2, 4) | |
| | | |[pic] |
| | | | |
| | | | |
| | |x | |
| | |3 | |
| | |4 | |
| | |3 | |
| | |5 | |
| | | | |
| | |f(x) | |
| | |7 | |
| | |-2 | |
| | |-7 | |
| | |-2 | |
| | | | |
|Write a Linear Equation from a |y = mx + b |Crystal gets paid $250 a week and $50 for every|Andy wants to mail a package. It costs $7 plus |
|Scenario | |computer she sells. Write an equation in |$0.25 for every ounce the package weighs. Write an |
| |m – increase or decrease |function notation that represents her weekly |equation in function notation that represents the |
| |b – starting point |income. |total cost of shipping the package. |
| | | | |
| | | | |
| | | | |
|Compare Linear Equations |Write 2 linear equations |Two companies are offering deals on leasing a new car. Toyota says that they will charge you $2000|
| |Graph the equations to find |to begin with and then you will pay $200 each month. Honda says that they will charge you $1000 to|
| |where they are the same |begin with but you will pay $400 each month. |
| |y = mx + b | |
| | |Write an equation for each company. |
| | |Toyota: Honda: |
| | | |
| | | |
| | |Which company has the greater rate of change? |
| | | |
| | | |
| | | |
| | |Which company had the lesser y-intercept? |
| | | |
| | | |
| | | |
| | |Which company is better for 5 months? |
| | | |
| | | |
| | | |
| | |When will it be cheaper to buy a car from Toyota? |
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| | | |
|Solve Consecutive Integer |Start with x. |3 consecutive integers add up to 123. Find the |Three consecutive EVEN integers add up to 336. Find|
|Problems |x + (x+1) + (x+2)+...= |three integers. |the integers. |
|Solve Perimeter Problems |Draw a picture |The width of a rectangle is 5 feet longer than |The length of a rectangle is nine inches more than |
| |Define your length and width |the length. The perimeter of the rectangle is |the width. The perimeter is 34 inches. Find the |
| |Add all 4 sides |110 feet. Find the length and the width. |length and width. |
| |Solve for both variables | | |
|Describe Characteristics of |Domain |Graph the funtion [pic] | |
|Linear Functions |Range | |Domain: __________ |
| |Y-int | | |
| |X-int | |Range: ___________ |
| |Inc/Dec | | |
| |Asymptote | |X-Int:________ Y-Int: _______ |
| |Rate of Change | |Inc or Dec |
| | | |RoC from x = 0 to 2: _______ |
|Solve for 2-variable Equations |ax + by = c |Gordon is going to buy fruit for a smoothie. He|Using your equation from #34, solve for R, the |
| |Never move the variable you’re|wants raspberries, R, that are $4 a carton and |number of raspberries. |
| |solving for. |strawberries, S, that are $2 a carton. Write an| |
| | |equation to represent all the combinations of | |
| | |fruit if Tony has $24 to spend. | |
| | | | |
| | | | |
| | | |If he buys 2 cartons of raspberries, how many |
| | | |strawberries can he buy? |
|Write and solve a system of |Define x and y. |Amy’s school is selling tickets to a choral |The band is selling wrapping paper for a |
|equations |Set up two equations. |performance. A senior citizen’s ticket is $3 |fundraiser. Customers can buy plain and shiny |
| |Decide the best method. |and a child’s ticket is $5. If they made $1450 |wrapping paper. Suzy bought 2 plain and 2 shiny |
| |Solve. |dollars and sold a total of 350 child and |rolls for $28. Oscar bought 4 plain and 1 shiny |
| | |senior citizen tickets, how many of each ticket|roll for $29. How much does each type of wrapping |
| | |did they sell? |paper cost? |
|Use the Recursive Form of an |Requires TWO parts. |Write the recursive rule for the sequence 9, 5,|Write the first 4 terms of the sequence a1= 5, an= |
|Arithmetic Sequence |a1= first term |1, -3, -7… |an-1 + 2 |
| |an= an-1 ± common difference | | |
|Use the Closed/Explicit Form of|Use the formula an = a1 + d(n |Write the explicit equation for the sequence |Write the first 5 terms of the sequence an = 3n –|
|an Arithmetic Sequence |– 1) |9, 5, 1, -3, -7… |4 |
| |Takes the form | | |
| |y = mx + b after being | | |
| |simplified |What is the domain and range of the sequence in | |
| | |#41? |What is the 200th term? |
| | | | |
|Write and Solve an Inequality |Pay attention to the direction|Yuri needs at least $1200 to pay for his car. He currently has $150. He makes $10 an hour at |
| |of the inequality sign. When |Subway and $15 an hour mowing lawns. |
| |multiplying or dividing by a | |
| |negative, switch the |Write an inequality that represents Yuri’s money needs. Use x for hours worked at Subway and y for|
| |direction. |hours mowing lawns. |
| |Shade on the graph to | |
| |represent ALL of the possible | |
| |solutions |If Yuri works 15 hours at Subway, how many hours does he need to work mowing lawns? |
| |Maximums and Minimums will be | |
| |found at the intercepts | |
| | |If Yuri works 30 hours mowing lawns, how many hours does he need to work at Subway? |
| | | |
| | | |
| | |Graph the inequality. |
| | |[pic] |
| | |What is the minimum number of hours that Yuri could work and still have enough money? |
| | | |
| | | |
|Graphing a system of linear |Make sure both equations are | [pic] | [pic] |
|inequalities. |in slope-intercept form. |[pic] | |
| |Decide if the lines will be | |[pic] |
| |solid or dashed. | | |
| |Graph the lines. | | |
| |Test a point-typically (0,0). | | |
| |Shade appropriately. | | |
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