COLLEGE ALGEBRA REVIEW FOR TEST 3

[Pages:10]COLLEGE ALGEBRA REVIEW FOR TEST 3

Use the given graph of f(x) = ax2 + bx + c to solve the specified inequality.

1) a) f(x) < 0 b) f(x) > 0

y

10

-10

-10

2) a) f(x) 0 b) f(x) 0

y 10

10 x

-10

10 x

-10

Solve the inequality. 3) x2 + 4x - 5 > 0

4) x2 - 3x - 4 < 0

5) -3x2 + 3x - 5 0

Use the given table for f(x) = ax2 + bx + c to solve the inequality f(x) < 0.

6) x -15 -12 -9 -6 -3 0 3

f(x) 45 0 -27 -36 -27 0 45

The given graph represents a translation of the graph of y = x2. Write the equation of the graph.

7)

y 10

5

-10

-5

-5

-10

5

10 x

Use transformations of the graphs of y = x2 or y = |x| to sketch a graph of f by hand.

8) f(x) = x - 5 - 2

9) f(x) = (x + 4)2 - 6

10) f(x) = -2(x - 3)2 - 1

Use the accompanying graph of y = f(x) to sketch the graph of the indicated equation.

11) y = f(x) - 3

y 10

5

-10

-5

-5

-10

5

10 x

Review for Test 3 12) y = -f(x)

y 10

5

-10

-5

-5

-10

5

10 x

13) y = f(-x)

y 10

(-2, 2)

-10 (2, -2)

10 x

-10

14) y = -

1 2

f(x)

y 10

-1(0-6, 0)

(0, 0)

(6, 0)10 x

(-3, -4) (3, -4)

-10

Answer the question. 15) How can the graph of f(x) = - x + 4 be obtained from the graph of y = x?

16) How can the graph of f(x) = -6x2 + 9 be obtained from the graph of y = x2?

Page 2 For the given representation of f, graph its reflection across the x-axis and the y-axis.

17) f(x) = x2 - 2x - 2

18) Line graph determined by the table x -8 -5 2 4 f(x) 6 1 2 -2

Two functions f and g are related by the given equation. Use the numerical representation of f to make a numerical representation of g.

19) g(x) = f(x) + 3

x 7 8 9 10 11 f(x) 16 18 20 22 24

Provide the requested response. 20) Use the graph of p(x) to determine the following:

y 4 3 2 1

-4 -3 -2 -1 -1 -2 -3 -4

1 2 3 4 5x

a) the number of turning points b) the x-intercepts c) the sign of the leading coefficient d) the minimum degree of p(x)

Determine any local or absolute extrema. 21) Use the graph of f to estimate the local extrema.

y 10 8 6 4 2

-5 -4 -3 -2 -1-2 -4 -6 -8 -10

12345 x

Review for Test 3 22) Determine any local or absolute extrema. a) f(x) = 3 - 4x b) g(x) = x2 + 2 c) h(x) = -3(x + 5)2 - 2

Use the graph to determine if f is odd, even, or neither. 23) a)

8y 6 4 2

-4 -3 -2 -1 -2 -4 -6

1 2 3 4x

-8

b)

20 y 15 10 5

-4 -3 -2 -1 -5

-10 -15 -20

1 2 3 4x

Solve the problem. 24) a) Complete the table if the function f is even. x -8 -4 4 8 f(x) -6 ? -2 ? b) Complete the table if the function g is odd. x -1 0 1 g(x) -9 ? ?

Determine whether the function is odd, even, or neither. 25) a) f(x) = 2x2 - 3 b) g(x) = 3x - 5 c) h(x) = -7x5 + 8x3 d) j(x) = 2x4 + 2x + 3

26) x -3 -2 -1 0 1 2 3 f(x) -29.0 -17 -5.01 5 -5.01 -17 -29.0

Page 3

Use

the

graph

of

f(x) =

1 2

x

-

x5

and

translations

of

graphs

to sketch the graph of the equation. 27) y = f(x) - 2

y 3

2

1

-3 -2 -1 -1 -2 -3

1 2 3x

28) y = -f(x - 2) + 1

y 3

2

1

-3 -2 -1 -1 -2 -3

1 2 3x

State the end behavior of the graph of f.

29) a) f(x) = x2 - 9x

b) g(x) = x2 + x3 + 6

c) h(x) = 2x3 - 1 - x4

d)

n(x) = 3x

-

1 6

x3

Review for Test 3 Pick which graph satisfies the given conditions.

30) Cubic polynomial with two distinct real zeros and a positive leading coefficient. A)

y

x

B)

y

x

C)

y

x

Page 4 31) Degree 4 with turning points at (-4, -20), (-2,

12) and (0, -20). A)

y

x

B)

y

x

C)

y

x

Evaluate the function f at the indicated value and graph

the function.

x2 - 2, if x < 2

32)

g(2) for g(x) =

4, if 2 x 4

1 2

x

+

5,

if

4

<

x

Divide. Write the answer with positive exponents only.

33)

20x11

-

12x10

- 16x9 4x9

+

32x7

+

7x5

Divide. 34) a) 4x2 - 37x + 63; x - 7 b) 2x4 - x3 - 15x2 + 3x; x + 3

Review for Test 3 Provide an appropriate response.

35) Use long division to express the (Dividend) as (Divisor)(Quotient) + (Remainder). 2x3 - 3x2 - 5x + 4 x - 2

Use synthetic division to divide the first polynomial by the second.

36) a) 5x3 + 16x2 + 8x - 8; x + 2 b) x5 + x3 + 4; x - 2 c) x4 - 3x3 + x2 + 7x - 9; x - 1

Solve the problem. 37) Use the figure to find the length L of the rectangle from its width and area A. Determine L when x = 3 feet.

2x + 1

A = 10x2 + 9x + 2

L

Use the given information about the polynomial function f(x) to write its complete factored form.

38) Degree 3; zeros: 3, 3, -2; leading coefficient = 1

39)

Degree

4;

zeros:

-

2 3

,

4,

-4,

-

3 2

;

leading

coefficient = 1

Write the complete factored form of the polynomial f(x), given the indicated zero.

40) a) f(x) = x3 + 2x2 - 11x - 12; -1 is a zero. b) g(x) = 3x3 + 4x2 - 28x + 16; -4 is a zero.

Page 5 The graph of the polynomial f(x) is shown in the figure. Estimate the zeros and state whether their multiplicities are odd or even.

41)

10 y

8

6

4

2

-5 -4 -3 -2 -1 -2 -4 -6 -8 -10

1 2 3 4 5x

42)

10 y 8 6 4 2

-5 -4 -3 -2 -1 -2 -4 -6 -8 -10

1 2 3 4 5x

Write a polynomial f(x) in complete factored form that satisfies the conditions. Let the leading coefficient be 1.

43) Degree 4; zeros: -3 with multiplicity 3, and 7 with multiplicity 1

Use the rational zero test to list all possible rational zeros of f(x), then find the zeros.

44) f(x) = 3x3 + 4x2 - 17x - 6

Solve the polynomial equation symbolically. 45) a) x3 - 4x = 0 b) 4x2 - 2x - 6 = 0 c) x3 - 5x2 + 6x = 0

Find the complete factored form of the polynomial f(x) that satisfies the given conditions. Then write the polynomial in expanded form.

46) Degree 2, leading coefficient 5, zeros at -4i and 4i

Review for Test 3

Find the zeros of f(x), given that one zero is k.

47) f(x) = x3 + 8x2 - 3x - 24

k = -8

48) f(x) = x3 - 9x2 + x - 9

k = 9

49) f(x) = x3 - 11x2 + 39x - 29

k = 1

50) f(x) = x4 - 5x2 - 36

k = -2i

Express f(x) in complete factored form. 51) a) f(x) = x2 + 16 b) g(x) = x2 + 3 c) h(x) = 5x3 + 5x d) p(x) = x3 + 9x2 + 9x + 81 e) q(x) = x4 + 2x3 - 11x2 + 8x - 60

Solve the polynomial equation. 52) x3 + 2x2 + 9x + 18 = 0

53) 3x4 - 15x3 + 30x2 - 60x + 72 = 0

Find the domain of f.

54) a)

f(x) =

17 11 - x

b)

g(x) =

x x2 +

2 9x

c)

h(x) =

(x - 3)(x + x2 - 1

3)

Find any vertical and horizintal asymptotes.

55) a)

f(x) =

7x + 4 2x - 1

b)

f(x) =

x - 6 x2 - 4

c)

f(x) =

6x3 + 3x - 3 x2 + 4x - 21

Write a symbolic representation of a rational function f that satisfies the conditions.

56) Vertical asymptotes x = 3 and x = -8, horizontal asymptote y = 3

Sketch the graph of the rational function.

57)

f(x)

=

x x

+

4 5

58)

f(x)

=

x2 - 16 x - 4

Page 6

Solve the equation.

59)

m

-

6 m

=

5

60)

1 b

+

b

1 -

4

=

b b -

3 4

Solve the rational equation.

61)

2 x

=

5x

x -

12

62)

5

x

x

+

3 4

=

7 x

Solve the polynomial inequality. 63) (x - 2)(x - 4)(x - 7) > 0

64) x3 + 8x2 + 17x -10

Use the graph of the rational function f to solve the inequality.

65) Solve f(x) > 0

y

6

4

2

-6 -4 -2 -2

-4

-6

2 4 6x

Solve the rational inequality.

66)

x x

+

4 1

>

0

67)

x

3 +

3

>

5 2

68)

x

8 -

3

x

6 -

1

Answer Key Testname: CAREVIEW3_F11

1) a) {x|-4 < x < 3} or (4, 3) b) {x|x < -4 or x > 3} or (-, -4) (3, )

2) a) {x|2 x 7} or [2, 7] b) {x|x 2 or x 7} or (-, 2] [7, )

3) x < -5 or x > 1 4) -1 < x < 4 5) All real numbers 6) -12 < x < 0 7) y = (x - 4)2 + 1 8)

y 10

5

-10

-5

-5

5

10 x

-10

9)

y 10

5

-10

-5

-5

5

10 x

-10

10)

y 10

5

-10

-5

-5

-10

5

10 x

11)

y 10

5

-10

-5

-5

5

10 x

-10

12)

y 10

5

-10

-5

-5

5

10 x

-10

13)

y 10

(2, 2)

-10 (-2, -2)

10 x

-10

Answer Key Testname: CAREVIEW3_F11

14)

y 10

(-3, 2) (3, 2) -10 (-6, 0) (0, 0) (6, 0) 10 x

-10

15) Shift it horizontally 4 units to the left and reflect it across the x-axis.

16) Stretch it vertically by a factor of 6, reflect it across the x-axis, and shift it 9 units upward.

17) x-axis: y = -x2 + 2x + 2

y 10 8 6 4 2

-10 -8 -6 -4 -2-2 -4 -6 -8 -10

2 4 6 8 10 x

y-axis: y = x2 + 2x - 2

y 10 8 6 4 2

-10 -8 -6 -4 -2-2 -4 -6 -8 -10

2 4 6 8 10 x

18) x-axis:

y 10 8 6 4 2

-10 -8 -6 -4 -2-2 -4 -6 -8 -10

2 4 6 8 10 x

y-axis:

y 10 8 6 4 2

-10 -8 -6 -4 -2-2 -4 -6 -8 -10

2 4 6 8 10 x

19) x 7 8 9 10 11 g(x) 19 21 23 25 27

20) a) 4 turning points b) -4, -3, 0, 2, 4 c) positive d) minimum degree = 5

21) Local maximum: approx. 8.08; local minima: approx. -7.67 and 2.75

22) a) No local extrema; no absolute extrema b) Local minimum: 2; absolute minimum: 2 c) Local maximum: -2; absolute maximum: -2

23) Odd, Even 24) a) -2, -6

b) 0, 9 25) a) Even b) Neither

c) Odd d) Neither 26) Even

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