University:
Winston-Salem Forsyth County Schools
Course:
AP Calculus AB
Academic year:

2014
Views:

155

Pages:

3
Author:

Adelyn Pacheco

Math 2 Name Unit 3A Test Review (Parent Functions, Transformations, Systems of Inequalities, Linear Programming) I. Parent Functions Matching: Match each function in 1-9 with the proper name 1. y = x² a. Reciprocal Function C2. y=x b. Constant Function 1 3. y=- c. Cube Root Function h_4. y=x² d. Absolute Value Function 95. y=x e. Quadratic Function 6. y= √x f. Square Root Function b7. y=c g. Identity Function 8. y= h. Cubic Function Short Answer: Write your answer on the line provided 9. Which of the above functions does not exist when x is zero? reciprocal function 10. If any of the above functions has a vertex, at what point is it located? (0,0) II. Algebraic Transformations Identify each parent function. Then describe the transformation. 11. f(x)=(x-3)² 12. f(x) = x²+4 13. f(x) = 2√x+1 Parent: 2. x quadratic Transformation: right 3 Parent: 3 X cubic Transformation: up4 Parent X square root vertical stretch. left I 14. f(x)=(x-7)-3 15. f(x)=+2 16. f(x)=-x² 3 Parent: x cubic Parent: 1x abs.val Transformation: right 7 down 3 Transformation: vert. shrink up 2 Parent: X quadratic 2 Transformation: reflect over x-axis Normally the vertex is at (0,0). Find the vertex of the following given the transformation. 17. f(x)=(x-7)-3 (1,3) 1 18. f(x)=x+1+2 2 (-1,2) 19. f(x)=(x-3) (3,0) III. Graphing Systems of Inequalities Graph each system. Shade the appropriate region. 20. y ≤2x-3 solid 21.x-2 dotled 22.y-x-2 dotted 1 •ys-x+2 Solid y2x+6 Solid 2 -2y4x-2 dotted y<2x-1 لا IV. Linear Programming Graph each the system of inequalities. Name the coordinates of the vertices of the feasible region. Find the minimum and maximum values of the given function. If it does not form a polygon, write "Unbounded". 23y22 *1≤x≤5 y5x+3 f(x,y)=3x-2y (x,y) 3x-2y f(x,y) (1,2) 3(1)-2(2) -1 (1,4) 3(1)-2(4) -5 (5,2) 3(5)-2(2) 11 (5,8) 3(5)-2(8)-1 min -5 (1.4) max 11 @ (5,2) لا 1 24. The Black and Gold gym is trying to plan its group fitness class schedule for Wednesdays. The gym manager has to take the following into account when planning this schedule. The gym only has enough teachers to offer at most 3 Zumba and at most 6 Cycling classes in one day. There is limited work out room space, so the gym can offer a total of at most 6 classes in one day. The gym makes a profit of $200 from each Zumba class and $300 from each Cycling class. X: Zumba y:cycling a. Write algebraic inequalities to represent this situation. (remember: you cannot offer less than zero classes) Inequality 1: 0≤x≤3 Inequality 2: 0≤ y= 6 Ineq 3: x+y=6 b. Graph the inequalities. c. The manager wants to make as much profit as possible. Write the objective function for this situation. f(x,y) = 200x+300 y d. Name the points outlining the feasible region. (0,0) (310) (016) (3,3) c. What schedule of classes will give the maximum profit? (show your work) (x,y) 200x+300y Ifa.y) ( 0,0) 200(0)+ 300(0) (3,0) 200(3)+300(0) 600 (0,6) 200(0)+300(6) 1800 (3,3) 200 (3)+300(3), 1500 O zumba and 6 cycling