Holiday Assignment

Name: ___________________________

Lomas MB43

Holiday Assignment State the domain

State the range

{(0,2), (0,4), (1, 2), (3, 4)}

{(1, 2), (1,1), (1, 0), (1, ­1)}

Write each relation as a set of ordered pairs. State the domain State the range of the relation.

State the domain State the range of the relation.

Is this a function? Why? Find r(­3).

Find g(3).   

g(x) = x² ­ 2x ­ 3

Is this a function? Why? {(3, 1), (2, 3), (1, 2), (3, 2)}

f(x) = x + 5 and g(x) = 4x,

h(x) = x² and p(x) = 2x ­ 3

Find g(f(0))

Find (p  h)(2) 0 

Find the rule of the composition (f  g)(x).

write the inverse {(0,6), (4, 2), (­1, 7), (­2, 8)}

write the equation of the inverse

f(x) = 6^x. f(3/2)

0 

f(x) = 3x + 2; g(x) = x ­ 3

y ­ 12 = 3x

Sketch the graph of y = 4^x in the interval ­ 2 ≤x ≤ 2.

1.

The function y = 2 x is equivalent to (1) x = y log 2 (2) x = log 2 y

2.

(3) y = x log 2 (4) y = log 2 x

What is the value of 2 −3 ? (1) (2)

3.

If log x 9 = −2, what is the value of x? (1) 81 (3) 3 (2)

1 81

(4)

1 3

4.

1 6 1 8

(3) -6 (4) -8

Find x to the nearest tenth. 5x = 3.6

5.

If log a = 2 and log b = 3, what is the numerical value 6. of log (1) 8 (2) –8

a b

3

?

If log a = x and log b = y , what is log a b ? (1) x + 2 y

(3) 25 (4) –25

(2) 2 x + 2 y

x+y 2 y (4) x + 2 (3)

7.

In the equation log x 4 + log x 9 = 2, x is equal to (1) 13 (3) 6.5 (2) 6 (4) 18

8.

Write in exponential form. 1.5 = log4 8

9.

Write in logarithmic form. 7² = 49

10 .

Find the value of x. log9 3 = x

11 .

Solve algebraically for x: 8 2 x = 4 6

12 .

Find the value of x. log6 X = 2

13 .

Solve for x: log b 36 − log b 2 = log b x

14 .

Solve for x to the nearest hundredth. log35 + log3x = log3(7 + x)

15 .

Solve for x: log b 36 − log b 2 = log b x

16 .

Solve for m: 3m+1 − 5 = 22

17 .

The number of houses in Central Village, New York, 18 grows every year according to the function . H(t ) = 540(1039 . ) t , where H represents the number of houses, and t represents the number of years since January 1995. A civil engineering firm has suggested that a new, larger well must be built by the village to supply its water when the number of houses exceeds 1,000. During which year will this first happen?

A population of wolves in a county is represented by the equation P(t ) = 80(0.98) t , where t is the number of years since 1998. Predict the number of wolves in the population in the year 2008.

1.

Which transformation is not an isometry? (1) rotation (2) line reflection

3.

5.

Which transformation represents a dilation?

6.

(8, 4)  (4,  8) (4) (8, 4)  ( 4, 2)

(1) (3,4) (2) (3-4)

8.

Which equation, when graphed on a Cartesian coordinate plane, would best represent an elliptical racetrack?

(3)

preserve

reflection

in

(4) rotation

(3) (2,5) (4) (5,2)

3 1 , ) 2 3

(1) (-6,12)

(3) (

(2) (-5,4)

(4) (-1,-8)

What is the equation of a circle with center (– 3,1) and radius 7?

( x  3) 2 (2) ( x  3) 2 (3) ( x  3) 2 (4) ( x  3) 2 10.

not

The image of the origin under a certain translation is the point (2,-6). The image of point (-3,-2) under the same translation is the point

(1)

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

does

When the point (2,-5) is reflected in the x-axis, what are the coordinates of its image? (1) (-5,2) (2) (-2,5)

(3)

What are the coordinates of the center of the circle represented by the equation ( x  3) 2  ( y  4) 2  25 ?

Which transformation orientation? (1) translation the y-axis (2) dilation

4.

(8, 4)  (11, 7) (2) (8, 4)  ( 8, 4)

9.

(3) dilation (4) translation

If point (5,2) is rotated counterclockwise 90° about the origin, its image will be point (1) (2, 5) (3) (-2, 5) (2) (2, -5) (4) (-5, -2)

(1)

7.

2.

 ( y  1) 2  ( y  1) 2  ( y  1) 2  ( y  1) 2

7  49 7  49

The accompanying diagram shows the graphs of a linear equation and a quadratic equation.

3x 2  10 y 2  288,000 (2) 3x  10 y  288,000 (3) 3x 2  10 y 2  288,000 (4) 30 xy  288,000 (1)

How many solutions are there to this system of equations? (1) l (3) 3 (2) 2 (4) 0

11.

What is one solution of the accompanying system of equations?

12.

y  x2  5

(1) –2 (2) 2

y  0.5x 2  3 (1) (3,5) (2) (0,5)

13.

15.

2 x 2  8 x  4  0 are

14.

imaginary real, rational, and equal real, irrational, and unequal real, rational, and unequal

Graph: 16x2 + 4y2 = 64

(3) 0 (4) 4

(3) (-2,1) (4) (0,3)

The roots of the equation (1) (2) (3) (4)

The roots of a quadratic equation are real, rational, and equal when the discriminant is

The roots for the equation (1) {1,-6} (2) {2,-3}

16.

x 2  5 x  6 are

(3) {-1,6} (4) {-2,3}

Find a)roots, b)turning point, and c)max or min y = x2 + 8x + 17

17.

On the accompanying grid, sketch the graphs of

y  2 x and

3y  7 x  3 over the interval − 3 ≤ x ≤ 4. Identify and state the coordinates of all points of intersection.

18.

Graph:

19 .

Use the diagram to find the tan x as a fraction in simplest form.

20.

A right triangle has a leg with a length of 6 inches and a hypotenuse of 10 inches. What is the length of the third side? [A] 8 in. [B] 7 in. [C] 9 in. [D] 6 in.

21. This is a sketch in standard position of which angle?

[A] -98° [C] 260°

23 .

22.

[B] -80° [D] 150°

Use special right triangles to find the coordinates of the point of intersection of the angle – 150° and the unit circle. Express your answer in fractions and radicals when necessary.

24.

25 .

26.

If sec θ = −3, what is the value of cos θ ? [A] 3             [B] −3 [C] 

27 .

29 .

31 .

1 1           [D] −  3 3

28.

Name the angle in standard position that is coterminal with –28°, also in standard position. Find the smallest such angle in the opposite direction of the given angle.

Given cos θ =

4 and csc θ > 0, find tan θ. 9

30.

Sketch the angle 329° in standard position.

32.

What is the exact value of tan 210° ?

33 .

35 .

37.

39 .

34.

Express as a function of an angle less than 45° tan 145°

If cos θ =

3 find the other 5 trigonometric values. 5

What is the reference angle of  ­149°?

36.

38.

40.

Express as a function of an angle less than 45° sin ­137°

What is the exact value of sec

4π ? 3

Solve for θ sec 2 θ = csc (2 θ -10)

What is the reference angle of  

5π ? 6

41.

A right triangle has a leg with a length of 6 inches and a hypotenuse of 10 inches. What is the length of the third side?

42.

(1) –42° (2) 222°

[A] 8 in. [B] 7 in. [C] 9 in. [D] 6 in.

43 .

45 .

If csc θ = −2, what is the value of sin θ ? 1 (1) -2 (3) − 2 1 (2) 2 (4) 2

44.

If (sec x – 2)(2 sec x – 1) = 0, then x terminates in (1) Quadrant I, only (2) Quadrants I and II, only (3) Quadrants I and IV, only (4) Quadrants I, II, III, and IV

46.

47. What

value

0° ≤ x ≤ 180°

3 tan x +1 =0 ?

(1) –30° (2) 30°

Which is an angle in Quadrant III with a reference angle of 42°?

The expression cos2 θ sin θ sin θ (2) cos2 θ (1)

(3) 318° (4) 138°

tan θ is equivalent to sec θ (3) cosθ (4) sin θ

If sin θ > 0 and sec θ < 0, in which quadrant does the terminal side of angle θ lie? (1) I (3) III (2) II (4) IV

of x in the interval 48. If tan θ = 2.7 and csc θ < 0, in which satisfies the equation quadrant does θ lie? (1) I (3) III (2) II (4) IV (3) 60° (4) 150°

49 .

50.

The expression to (1) 1 (2) -1

51.

53 .

Given cos θ =

4 and sin θ > 0, find tan θ. 9

1 − cos 2 x is equivalent sin 2 x

(3) sin x (4) cos x

52.

Solve. Find all solutions from 0° to 360°. 3sin x = 1

54.

Solve. Find all solutions from 0° to 360°. 3cos² x + 4 cos x = 1

55 .

Verify cos θ tan θ = sin θ

57. Verify:

sin θ (csc θ - sin θ) = cos² θ

56.

Solve. Find all solutions from 0° to 360°. 3sin2 θ + sin θ = 10

58.

Solve. Find all solutions from 0° to 360°. 3tan x - 4 = 7