Alg 2 Midterm Review Part 2 Name_________________ Unit Three (Sections 2.1, 2.2, 2.4, 2.7, 3.1, 3.3, 3.4) Find the domain and range of each of the following relations. Indicate if the relation is a function. 1) K={(9,1), (‐2, 1), (0, 4)} 2) P={(3,5), (5, 2), (3, ‐2)} 3) 4) Create a mapping of relation P from number 2 above. 5) Create two separate graphs one in which the relation is… (A) a function (B) not a function 6) Given the graph below: (A) Find the slope of the line (B) Find the coordinates of the y‐intercept? 7) Graph: 2x – 3y =12 3
8) Graph: y  x  4 2
9) Find the slope of the line between the points: (‐2, 4) and (1,‐5) 10) Find the slope of the line in the equation: 7x + 2y = ‐18 11) Given the equation: 3x + 9 = 5y (A) Find the slope of the line (B) Find the slope of a line parallel to the given line (C) Find the slope of a line perpendicular to the given line 2
12) Graph: y   x  5
3
13) Graph: 4 y  2 x  10 In each of the following, use the given information to write the equation of the line in (A) Point‐Slope form and (B) Slope‐Intercept form 14) P(‐8, 5) and m = 4 15) 16) Write the equation of the line, in slope‐intercept form, parallel to y = 2x + 1 going through ( ‐1, 3 ). 17) Write the equation of the line, in slope‐intercept form, perpendicular to y = ‐ 4x + 3 going through (12, ‐1 ) 18) A 3‐mi cab ride costs $3.00. A 6‐mi cab ride costs $4.80. (A) Find a linear equation that models cost of a cab ride (B) Use the model to find the cost of a 7 mi cab ride. 19) The number of hours 12 students watched television during the weekend and the scores of each student who took a quiz the following Monday. TV hours 0 1 2 Scores 96 85 82 10 5 6 7 3 5 3 7 5 50 68 58 65 74 76 95 75 84 y
A) Graph the scatter plot and best‐fit line on your scatter plot. B) What type of correlation is this? C) Use your TI‐Calculator to find the line of best fit. How accurate is this line? D) Use your equation to determine if a person watched 8 hours of TV, what would they score on the quiz? x
20) Write an inequality for the graph: y  2 x  6
22) Graph: 
 x  4 y  8
21) Write an inequality for the graph: 23) Find the values of x and y that maximize the objective function P = 3x + 2y for the graph. What is the maximum value? 24) Given the system of constraints, name all vertices. Then find the maximum value of the given objective function: C = 4x – 3y x  0
y  0


x
y
6

2

12

4 y  4 x  8
**Use a separate sheet of graph paper and a straightedge to complete this problem.** 25) A fish market buys tuna for $.50 per pound and spends $1.50 per pound to clean and package it. Salmon costs $2.00 per pound to buy and $2.00 per pound to clean and package. The market makes $2.50 per pound profit on tuna and $2.80 per pound profit for salmon. The market can spend only $106 per day to buy fish and $134 per day to clean it. How much of each type of fish should the market buy to maximize profit? A) Write the objective function for the given situation B) Write the constraints for the given situation Unitt Four (Secctions 5.1 –
– 5.3) Determine whether each functtion is linear o
or quadratic. Identify the quadratic, lin
near, and con
nstant terms.
1. y = x² ‐ x + 7 2. f(x) =
= (2x + 4)3x
3. f(xx) =5x² + 2x –
– 6 + 7x – 5x² 4. y = 7(x – 6) + 42
5. Identify the vertex and the aaxis of symmetry of the parabola. Identify pointts correspond
ding to P and
d Q. Identtify the vertexx, axis of sym
mmetry and th
he y‐interceptt of the graphh of the function 6. y = 3x² + 6x + 7
7 7. f(x) = 2(xx + 1)² + 3 Grap
ph the following parabolas. Show the ve
ertex and axis of symmetrry in each graph. 8. yy = ‐x² + 4x + 2
2 9. y = (x + 3)² ‐ 2
2 11.. y = ‐2(x – 2)²² + 5 10. yy = ½ x ² ‐ 2