Assignment 4 Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the power function that the graph of f resembles for large values of |x|. 1) 1) f(x) = (x - 4 ) 3 A) y = x 3 B) y = x - 4 C) y = x 12 D) y = x - 64 State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. 2) 2) f(x) = x(x - 15 ) A) Yes; degree 1 B) Yes; degree 0 C) No; it is a product D) Yes; degree 2 For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x - axis at each x - intercept. 3) 3) f(x) = 3 ( x 2 + 1 ) ( x 2 + 3 ) 2 A) - 1 , multiplicity 1, crosses x - axis; - 3 , multiplicity 2, touches x - axis B) No real zeros C) 1 , multiplicity 1, crosses x - axis; - 1 , multiplicity 1, crosses x - axis; 3 , multiplicity 2, touches x - axis; - 3 , multiplicity 2, touches x - axis D) - 1 , multiplicity 1, touches x - axis; - 3 , multiplicity 2, crosses x - axis 4) f(x) = 1 2 x 4 ( x 2 - 5 )(x + 1 ) 4) A) 0, multiplicity 4 , crosses x - axis; - 1 , multiplicity 1, touches x - axis B) 0, multiplicity 4 , crosses x - axis; - 1 , multiplicity 1, touches x - axis; 5 , multiplicity 1, touches x - axis; - 5 , multiplicity 1, touches x - axis C) 0, multiplicity 4 , touches x - axis; - 1 , multiplicity 1, crosses x - axis; 5 , multiplicity 1, crosses x - axis; - 5 , multiplicity 1, crosses x - axis D) 0, multiplicity 4 , touches x - axis; - 1 , multiplicity 1, crosses x - axis Find the power function that the graph of f resembles for large values of |x|. 5) 5) f(x) = (x + 5 ) 2 A) y = x 5 B) y = x 2 C) y = x 25 D) y = x 10 State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. 6) f(x) = x 3 - 4 x 5 6) A) Yes; degree - 5 B) Yes; degree 5 C) Yes; degree 3 D) No; it is a ratio of polynomials Use transformations of the graph of y = x 4 or y = x 5 to graph the function. 1
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Assignment 4 MULTIPLE CHOICE. Choose the one alternative ...
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Assignment 4Name___________________________________MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the power function that the graph of f resembles for large values of |x|.
1) 1)f(x) = (x - 4)3
A) y = x3 B) y = x-4 C) y = x12 D) y = x-64
State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.
2) 2)f(x) = x(x - 15)
A) Yes; degree 1 B) Yes; degree 0
C) No; it is a product D) Yes; degree 2
For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis ateach x -intercept.
Find the power function that the graph of f resembles for large values of |x|.
5) 5)f(x) = (x + 5)2
A) y = x5 B) y = x2 C) y = x25 D) y = x10
State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.
6) f(x) =x3 - 4
x5 6)
A) Yes; degree -5 B) Yes; degree 5
C) Yes; degree 3 D) No; it is a ratio of polynomials
Use transformations of the graph of y = x4 or y = x5 to graph the function.
1
7) 7)f(x) = -2(x - 4)4 + 4
A) B)
C) D)
2
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Analyze the graph of the given function f as follows:(a) Determine the end behavior: find the power function that the graph of f resembles for large values of |x|.(b) Graph f using a graphing utility.(c) Find the x- and y-intercepts of the graph.(d) Determine whether the graph crosses or touches the x-axis at each x-intercept.(e) Use the graph to determine the local maxima and local minima, if any exist. Round turning points to two decimalplaces.(f) Use the information obtained in (a) - (e) to draw a complete graph of f by hand. Label all intercepts and turningpoints.(g) Find the domain of f. Use the graph to find the range of f.(h) Use the graph to determine where f is increasing and where f is decreasing.
8) 8)f(x) = x2(x + 3)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use transformations of the graph of y = x4 or y = x5 to graph the function.
9) 9)f(x) = (x + 5)4
A) B)
3
C) D)
Find the x- and y-intercepts of f.
10) 10)f(x) = -x2(x + 4)(x2 + 1)
A) x-intercepts: -4, -1, 0; y-intercept: 4 B) x-intercepts: -4, -1, 0; y-intercept: -4
34) What is the domain of the function f(x) =x - 3x + 8
? 34)
A) [3, ) B) ( , -8) [3, ) C) ( , -8) D) ( , -8) (3, )
Solve the inequality algebraically. Express the solution in interval notation.
35) (x - 7)(x + 7)x
0 35)
A) (- , -7] (0, 7] B) [-7, 0) [7, ) C) [-7, 0) (0, 7] D) (- , -7] [7, )
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36) (8 - x)3(8x - 3)x3 + 8
< 0 36)
A) 38
, 2 (8, ) B) -8, 38
(2, ) C) (-2, 8) 38
, D) -2, 38
(8, )
Solve the problem.
37) 37)What is the domain of the function f(x) = x4 - 16 ?
A) ( , 2) (2, ) B) ( , -2] [2, ) C) ( , -2) (2, ) D) ( , 2)
Solve the inequality algebraically. Express the solution in interval notation.
38) 38)x4 - 21x2 - 100 > 0
A) (- , -5) (5, ) B) (- , -5) (-2, 2) (5, )
C) (-5, 5) D) (-5, -2) (2, 5)
Solve the inequality by using the graph of the function.
39) f(x) < 0, where f(x) =-4
(x - 1)(x + 5). 39)
A) (- , -5] [1, ) B) [-5, 1] C) (-5, 1) D) (- , -5) (1, )
Solve the inequality algebraically. Express the solution in interval notation.
40) 9x - 3x + 8
8 40)
A) (-8, 67) B) (-8, 11) C) (-8, 67] D) (-8, 11]
Use the Factor Theorem to determine whether x - c is a factor of f. If it is, write f in factored form, that is, write f in theform f(x) = (x - c)(quotient).