AnswersSem 2 - Algebra 2 with Probability - Nkwati - ContentUnit Test

Unit Test — Unit test Answers

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The owner of a coffee shop chain creates a graph representing sales in thousands of dollars. She describes the characteristics as follows:• There have been two turning points in sales this year.• Sales are expected to increase in the long run.• The least amount of sales during the year is about $250,000.Which graph correctly shows the coffee shop’s sales?

A
mc025-1.jpg
Option A
B
mc025-2.jpg
Option B
C
mc025-3.jpg
Option C
D
mc025-4.jpg
Option D
2
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Let a, b, and c be real numbers where a b c 0. Which of the following functions could represent the graph below?

Question illustration
A
f(x) = x2(x – a)2(x – b)4(x – c)
B
f(x) = x3(x – a)3(x – b)(x – c)2
C
f(x) = x4(x – a)(x – b)3(x – c)3
D
f(x) = (x – a)2(x – b)(x – c)6
3

What are the possible degrees for the polynomial function?

Question illustration
A
degrees of 6 or greater
B
even degrees of 6 or greater
C
degrees of 5 or greater
D
odd degrees of 5 or greater
4

Which best describes the end behavior of ?

Question illustration
A
As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) increases.
B
As x > 0 increases, f(x) decreases. As x < 0 decreases, f(x) decreases.
C
As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) decreases.
D
As x > 0 increases, f(x) decreases. As x < 0 decreases, f(x) increases.
5

A polynomial function has a root of –3 with multiplicity 2, a root of 0 with multiplicity 1, a root of 1 with multiplicity 1, and a root of 3 with multiplicity 2. If the function has a positive leading coefficient and is of even degree, which could be the graph of the function?

A
mc015-1.jpg
Option A
B
mc015-2.jpg
Option B
C
mc015-3.jpg
Option C
D
mc015-4.jpg
Option D
6

What are the solutions of the equation (2x + 3)2 + 8(2x + 3) + 11 = 0? Use u substitution and the quadratic formula to solve.

A
x = StartFraction negative 4 plus-or-minus StartRoot 5 EndRoot Over 2 EndFraction
Option A
B
x = StartFraction negative 7 plus-or-minus StartRoot 5 EndRoot Over 2 EndFraction
Option B
C
x = –7 and x = –2
D
x = –1 and x = 4
7

The formula for the volume of a cylinder with a height of 5 units is where r is the radius of the cylinder. What is the domain and range of this function?

Question illustration
A
r < 0, V(r) < 0
B
r > 0, V(r) < 0
C
r 0
D
r > 0, V(r) > 0
8

The polynomial function is graphed below.Which is a potential rational root of f(x) at point P?

Question illustration
A
The root at point P may be .
Option A
B
The root at point P may be .
Option B
C
The root at point P may be .
Option C
D
The root at point P may be .
Option D
9

The square root of a number is greater than the square of the number. For what set of numbers is this true?

A
(0, 1)
B
[0, 1]
C
[1, ꝏ)
D
(1, ꝏ)
10

Which of the following is the complete list of roots for the polynomial function ?

Question illustration
A
–3 + 2i, –3 – 2i
B
–2, –4
C
–2, –4, –3 + 2i, –3 – 2i
D
–2, –4, –3 + 2i, 3 + 2i
11

Which statement best describes the equation (x + 5)2 + 4(x + 5) + 12 = 0?

A
The equation is quadratic in form because it can be rewritten as a quadratic equation with u substitution u = (x + 5).
B
The equation is quadratic in form because when it is expanded, it is a fourth-degree polynomial.
C
The equation is not quadratic in form because it cannot be solved by using the quadratic formula.
D
The equation is not quadratic in form because there is no real solution.
12

Which statement describes the graph of this polynomial function?

Question illustration
A
The graph crosses the x-axis at x = 0 and touches the x-axis at x = 3.
B
The graph touches the x-axis at x = 0 and crosses the x-axis at x = 3.
C
The graph crosses the x-axis at x = 0 and touches the x-axis at x = –3.
D
The graph touches the x-axis at x = 0 and crosses the x-axis at x = –3.
13

The graphs of two polynomial equations do not intersect. Kelly concludes that the system has no solution. Which statement best explains why Kelly’s reasoning is correct or incorrect?

A
She is incorrect because systems may have only complex solutions which are not visible on a graph.
B
She is incorrect because the solutions may have multiplicity greater than 1.
C
She is correct because all solutions are intersection points of the graphs.
D
She is correct because the solutions are irrational.
14

According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 5x3 – 7x + 11?

A
, , , 5
Option A
B
, 1, , 11
Option B
C
, , , , , 5, 11
Option C
D
0, , , , , , 5, 11
Option D
15

How many integers satisfy the inequality (x 2 – 4)(x 2 – 10) < 0?

A
none
B
two
C
four
D
an infinite number
16

What are the roots of the polynomial equation ? Use a graphing calculator and a system of equations.

Question illustration
A
–6, 6
B
–4, 1, 3
C
–3, –1, 4
D
1, 3
17

If (x – 2k) is a factor of f(x), which of the following must be true?

A
f(2k) = 0
B
f(–2k) = 0
C
A root of f(x) is x = –2k.
D
A y intercept of f(x) is x = 2k.
18

The price that a company charged for a basketball hoop is given by the equation where x is the number of hoops that are produced, in millions. It costs the company $30 to make each basketball hoop. The company recently reduced its production to 1 million hoops but maintained its profit of 15 million dollars. Approximately how many basketball hoops did the company previously produce to make the same profit?

Question illustration
A
1.3 million hoops
B
1.4 million hoops
C
15 million hoops
D
30 million hoops
19

Use synthetic division to solve (x4 – 1) ÷ (x – 1). What is the quotient?

A
x cubed minus x squared + x minus 1
Option A
B
x3
C
x cubed + x squared + x + 1
Option C
D
x3 – 2
20

The formula for the volume of a cube is V(s) = s3 where s is the side length of the cube. What is the domain and range of this function?

A
s < 0, V(s) < 0
B
s > 0, V(s) < 0
C
s 0
D
s > 0, V(s) > 0

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