June 2018 Common Core Algebra I Regents, Part II

The following are some of the multiple questions from the recent June 2018 New York State Common Core Algebra I Regents exam.
The answers to Part I can be found here

June 2018 Algebra I, Part II

Each correct answer is worth up to 2 credits. Partial credit can be given. Work must be shown or explained.

25. Graph f(x) = SQRT(x+2) over the domain -2 < x < 7.

Answer:
See graph below. The domain has two closed endpoints. No arrows. You only needed to plot the integer points
Note that this is an often-repeated question, with the graph translated.

26. Caleb claims that the ordered pairs shown in the table below are from a nonlinear function.

x	f(x)
0	2
1	4
2	8
3	16

State if Caleb is correct. Explain your reasoning.

Answer:
Caleb is correct. The table does not have a constant rate of change so it cannot be linear.
That is all that is required. Everything below is extra information. Note that if you make a mistake with anything that follows you could lose a point.
Proof: (4 - 2)/(1 - 0) = 2/1 = 2; (8 - 4)/(2 - 1) = 4/1 = 4

In fact, this is an exponential function because it has a common ratio:
Proof: 4/2 = 2; 8/4 = 2; 16/8 = 2.

27. Solve for x to the nearest tenth: x² + x - 5 = 0.

Answer:
You can solve this using the Quadratic Formula or by Completing the Square. To complete the square would involve fractions (1/2 and 1/4), so let's use the Quadratic Formula. See image below.

Since the question did not say "calculate" or "algebraically", you also could have done this graphically. You could use your graphing calculator to graph the equation, and then use the Zeroes function. You would have to state this in some manner to justify your answer, because simply listing x = 1.8 or x = -2.8 as the answer is only worth 1 point.

28. The graph of the function p(x) is represented below. On the same set of axes, sketch the function p(x + 2).

Answer:
p(x + 2) shifts p(x) two units to the left.
For example, when x = 0, p(0 + 2) = p(2) = 2. So (0, 2) is a point on the graph. See image below.

29. When an apple is dropped from a tower 256 feet high, the function h(t) = - 16t² + 256 models the height of the apple, in feet, after t seconds. Determine, algebraically, the number of seconds it takes the apple to hit the ground.

Answer:
Set the equation equal to 0 and then use inverse operations. Discard the negative square root.

-16t² + 256 = 0
-16t² = -256
t² = 16
t = 4 seconds.

30. Solve the equation below algebraically for the exact value of x.

6 - (2/3) (x + 5) = 4x

Answer: You can get rid of the fraction by multiplying the entire equation by 3.

6 - (2/3) (x + 5) = 4x
(3)[6 - (2/3) (x + 5)] = [4x](3)
18 - 2(x + 5) = 12x
18 - 2x - 10 = 12x
8 - 2x = 12x
8 = 14x
x = 8/14 or x = 4/7
Since the wanted an exact value, leave the answer in fraction form because it's a repeating decimal. DO NOT ROUND.

31. Is the product of SQRT(16) and 4/7 rational or irrational? Explain your reasoning.

Answer:
The product is rational because the square of 16 is 4, which is rational, and 4/7 is rational. The product of two rational numbers is always rational.
In this case, the product is 16/7, which is a ratio of two integers.

32. On the set of axes below, graph the piecewise function:

Answer:
To graph this piecewise function, you need to graph f(x) = -1/2x, but only for the domain x < 2. The "Less than" sign indicates that 2 is NOT part of the domain, so f(2) = -1/2(2) = -1 is a BOUNDARY. In other words, you must graph this point, but with an open circle. Do not fill it in. Have an arrow on the left side only.
For the rest of the graph, for the domain x > 2, graph f(x) = x. That is (2, 2), (3, 3), (4, 4), etc. Closed endpoint on the left, arrow on the right.
See graph below.

End of Part II

How did you do?

Questions, comments and corrections welcome.