Trigonometry/Pre-Calculus Chapter 2 Test

Multiple Choice
Identify the choice that best completes the statement or answers the question.

____	1.	Determine whether the following graph represents the graph of polynomial function. Explain your reasoning.

A)	yes; no breaks, no corners, end behavior like a polynomial	
B)	no; has a break	
C)	no; has a corner	
D)	yes; no breaks, having corners, end behavior is not like a polynomial	
E)	yes; having breaks, having corners, end behavior like a polynomial	

____	2.	Determine whether the function  is a polynomial function. If so, find the degree. If not, state the reason.
A)	No, because this function cannot be written as a sum of terms in which t is raised to a non-negative integer power.	
B)	No, because this function can be written as a sum of terms in which t is raised to a non-negative integer power.	
C)	Yes, and the degree is 13.	
D)	Yes, and the degree is .	
E)	No, because this function cannot be written as a sum of terms in which t is raised to a non-positive real power.	

____	3.	Determine whether the function  is a polynomial function. If so, find the degree. If not, state the reason.
A)	No, because this function cannot be written as a sum of terms in which x is raised to a non-negative integer power.	
B)	No, because this function can be written as a sum of terms in which x is raised to a non-negative integer power.	
C)	Yes, and the degree is 8.	
D)	Yes, and the degree is 0.	
E)	Yes, and the degree is 5.	

____	4.	Determine the end behavior of the function .
A)	the end behavior of the function cannot be determined	
B)	 as  as 	
C)	 as  as 	
D)	 as  as 	
E)	 as  as 	

____	5.	Sketch the polynomial function .
A)		
B)		
C)		
D)		
E)		

____	6.	Find the interval(s) on which the value of the function  is positive.
A)		
B)		
C)		
D)		
E)		

____	7.	Sketch the graph of the polynomial function .
A)		
B)		
C)		
D)		
E)		

____	8.	For the polynomial function graphed below, find whether the power of the leading term is odd or even.

A)	odd	
B)	even	

____	9.	Find the end behavior of the function .
A)	 as  as 	
B)	 as  as 	
C)	 as  as 	
D)	 as  as 	
E)	the end behavior of the function cannot be determined	

____	10.	Find the y-intercept of the function .
A)	y-intercept: (4, 0)	
B)	y-intercept: (0, 4)	
C)	y-intercept: (2, 0)	
D)	y-intercept: (0, 2)	
E)	y-intercept: (0, 0)	

____	11.	Find the intervals on which the function  is positive or negative.
A)		
B)		
C)		
D)		
E)		

____	12.	Find the real zeros of the polynomial function  by factoring.
A)		
B)		
C)		
D)		
E)		

____	13.	Find an expression for a polynomial function f(x) having degree 3; zeros , 5, and 6, each of multiplicity 1.
A)		
B)		
C)		
D)		
E)		

____	14.	Approximate the values of x at which a local maximum or local minimum occurs for the polynomial function  whose graph is given below. Round your answer to two decimal places.

A)	local maximum: 1.29; local minimum: 	
B)	local maximum: ; local minimum: 6.30	
C)	local maximum: 6.30; local minimum: 2.30	
D)	local maximum: –; local minimum: 1.29	
E)	local maximum: 1.29; local minimum: 6.30	

____	15.	Use long division to divide.

A)		
B)		
C)		
D)		
E)		

____	16.	Use synthetic division to divide.

A)		
B)		
C)		
D)		
E)		

____	17.	Use synthetic division to divide.

A)		
B)		
C)		
D)		
E)		

____	18.	Use synthetic division to divide  by .
A)		
B)		
C)		
D)		
E)		

____	19.	Use synthetic division to find  for  and .
A)		
B)		
C)		
D)	391	
E)	419	

____	20.	Determine whether q(x) is a factor of p(x). Here,  and . Justify your answer.
A)	no,  has a non-zero remainder	
B)	no,  has a non-zero remainder	
C)	no,  has no remainder	
D)	yes,  has no remainder	
E)	yes,  has a non-zero remainder	

____	21.	Find the remainder when  is divided by .
A)	4	
B)	8	
C)	5	
D)	6	
E)	7	

____	22.	Identify the zeros of the polynomial .
A)		
B)		
C)	4	
D)	7	
E)	3	

____	23.	Identify a zero of the polynomial .
A)		
B)		
C)		
D)		
E)		

____	24.	Use the zero  to completely factor the polynomial .
A)		
B)		
C)		
D)		
E)		

____	25.	Find all the real zeros of .
A)		
B)		
C)		
D)		
E)		

____	26.	Find all the real zeros of .
A)		
B)		
C)		
D)		
E)		

____	27.	Find all the rational zeros of the function .
A)		
B)		
C)		
D)		
E)		

____	28.	Find all real solutions of the polynomial equation .
A)	, and 	
B)	 and 	
C)	 and 	
D)	 and 	
E)	a nd 	

____	29.	Determine the domain of the function .
A)	all real numbers except 	
B)	all real numbers except 	
C)	all real numbers except 	
D)	all real numbers except 	
E)	all real numbers	

____	30.	Determine the domain of .
A)	all real numbers except 	
B)	all real numbers except 	
C)	all real numbers except 	
D)	all real numbers except 	
E)	all real numbers	

____	31.	Find the domain of .
A)	all real numbers except 	
B)	all real numbers except 	
C)	all real numbers except 	
D)	all real numbers except 	
E)	all real numbers	

____	32.	The graph of a rational function is given below. Find the domain for the function.

A)		
B)		
C)		
D)		
E)		

____	33.	The graph of a rational function is given below. Find the vertical and horizontal asymptotes of the graph of the function.

A)	vertical asymptote: ; horizontal asymptote: 	
B)	vertical asymptote: ; horizontal asymptote: 	
C)	vertical asymptote: ; horizontal asymptote: 	
D)	vertical asymptote: ; horizontal asymptote: 	
E)	vertical asymptote: ; horizontal asymptote: 	

____	34.	For the function  find the values of , and .
x	10	50	100	1000	
	6.94	6.9976	6.9994	6.999994	

A)	 as 	
B)	 as 	
C)	 as 	
D)	 as 	
E)	 as 	

____	35.	Which of the following is the graph of the given equation?

A)		
B)		
C)		
D)		
E)