25. Graph the function y = |x - 3| on the set of axes below.
Explain how the graph of y = |x - 3| has changed from the related graph y = |x|.
This absolute value graph is V-shaped, with a slope of -1 on the left side and 1 on the right side. It's vertex is at (3, 0).
The change from y = |x| is that the graph has shifted three units to the right.
26. Alex is selling tickets to a school play. an adult ticket costs $6.50 and a student ticket costs $4.00. Alex sells x adult tickets and 12 student tickets. Write a function f(x), to represent how much money Alex collected from selling tickets.
f(x) = 6.50x + 4.00(12) or
f(x) = 6.50x + 48.00
27. John and Sarah are each saving money for a car. The total amount of money John will save is given by the function F(x) = 60 + 5x. The total amount of money Sarah will save is given by the function g(x) = x2 + 46. After how many weeks, x, will they have the same amount of money? Explain how you arrived at your answer.
One way: Enter y1 = 60 + 5x and y2 = x2 + 46 into your graphing calculator and look at the Table of Values. Copy the Table of Values onto your paper (and explain that this is what you did).
Second way: Solve the following quadratic equation: x2 + 46 = 60 + 5x
x2 - 5x - 14 = 0
(x - 7)(x + 2) = 0
x = 7 or x = -2
Throw out -2 as irrelevant. In seven weeks the amounts will be the same.
28. If the difference (3x2 - 2x + 5) - (x2 +3x - 2) is multiplied by 1/2X2, what is the result, written in standard form.
The subtraction gives you 2x2 - 5x + 7. Times 1/2x2 gives x4 - 2.5x3 + 3.5x2.
29. Dylan invested $600 in a savings account at 1.6% annual interest rate. He made no deposits or withdrawals on the account for 2 years. The interest was compounded annually. Find, to the nearest cent, the balance in the account after 2 years.
Because it is only 2 years, you have your choice of using the compound interest formula (exponential growth) or using the simple interest formula, adding the interest and using the simple interest formula a second time on the new amount (the principal). The second method takes longer, but is good if you forgot the first formula.
The formula given in the reference table is overly complex -- it's like that because you'll need that one in the future. On the other hand, the example in question 17 in Part 1 is a better example to use.
(600)(1.016)2= 619.3536 = $619.35
Or (600)(1.016) = 609.60 and (609.60)(1.016) = 619.3536 = $619.35
30. Determine the smallest integer that makes -3x + 7 - 5x < 15 true.
-8x + 7 < 15
-8x < 8
x > -1
The smallest integer that makes this statement true is 0 (because it has to be greater than -1).
31. The residual plots from two different sets of bivariate data afe graphed below.
Explain, using evidence from graph A and graph B, which graph indicates that the model for the data is a good fit.
FOR MORE INFORMATION ABOUT RESIDUALS, CHECK OUT MY PREVIOUS POST ABOUT THE QUESTION FROM THE AUGUST 2014 REGENTS EXAM.
Basically, Graph A is a better model because the residuals are scattered about and there is no pattern to them. Graph B is not a good fit because the residuals form a pattern, which is sort of a curve. This can happen, for example, when a linear model (linear regression) is used but a quadratic regression would be better. (You don't need the last sentence -- only the part about why A is good and B is bad.)
32. A landscaper is creating a rectangular flower bed such that the width is half of the length. The area of the flower bed is 34 square feet. Write and solve an equation to determine the width of the flower bed, to the nearest tenth of a foot.
A = L * W = 34. L = 2W
(2W)(W) = 34
2W2 = 34
W2 = 17
W = SQRT(17) = 4.123105626 = 4.1 feet.
That's it for Part II. Hopefully, I'll have Part III up Sunday or Monday.
Happy Fathers Day to all your Fathers (and to you, too, if you are a Father).