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Mathematics III
1st Indicative Exam Requirement
Chapter 1 Relations and Functions
I.

Determine the domain of the following functions
1. d(y) = y + 3
2
2. g(k) = 2k + 4k - 6
3.

b(n) =

4.

m(t ) = −2 + 9 − x 2

5.

u( x ) =

6.
II.

2n − 8

8.

x−5
2x + 4
1
a (r ) = r +
r −1

2
c + 3c
x
f ( x) =x+3

y (c ) =

2

9.

t ( v ) = v 2 + 2v − 8

10.

n(t ) =

Find the domain of the following graphs
11.
12.

14.

III.

7.

t
1+ t

13.

15.

16.

Determine if the followings are functions or not, explain your reasoning
17. {(4, –5), (0, –9), (1, 0), (7, 0)}
18. {(–2, –3), (6, –8), (4, 2), (6, –5), (2, –5)}
19. {(5, –12), (–1, –2(\), (8, –5), (4, –2), (3, –5)}20. {(5, 2), (–2, 15), (–7, 15), (1, 5), (4, 15), (–7, 2)}

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22.

21.

25.

IV.

26.

23.

24.

27.

28.

Perform the following operations with functions

f ( x) = 5 x + 4
29. ( f + g )( x )
30. ( f − g )( x )
31. ( f ⋅ g )( x )

g ( x) = 4 − x

f
 ( x )
g
33. ( g o f )( x )
34. ( f + g )(3)
32.

f ( x) = 2 x 2 − 3x + 4
35. ( f + g )( x )
36. ( f − g )( x )
37. ( f ⋅ g )( x )

g ( x) = x + 3

f
 ( x )
g

39. ( f o g )( x )
40. ( f + g )(3)
38.

Chapter 2 The Linear Function
V.

VI.

VII.

Using points A(–10, 6), B(–5, 8) find:
41. Slope
42. y and x-intercepts
43. Graph

44. Point-slope form equation
45.Slope-intercept form equation
46. General form equation

Using points A(–4, –2), B(4, 0) find:
47. Slope
48. y and x-intercepts
49. Graph

50. Point-slope form equation
51. Slope-intercept form equation
52. General form equation

Solve the following problems
53. Write the slope-intercept form of an equation of the line that passes through point (3, 1) and is parallel
to the graph of2x + y – 5 = 0 and draw its graph.
54. Write the slope-intercept form of an equation of the line that passes through point (2, 4) and is
perpendicular to the graph of x – 6y – 2 = 0 and draw its graph.
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55. Write the general form of an equation of the line that passes through point (–1, –2)and is parallel to
the graph of 3x – y – 5 = 0 and draw its graph.
56. Write the general form of an equation of the line that passes through point (–4, 1) and is perpendicular
to the graph of 4x + 7y – 6 = 0 and draw its graph.
57. Flourishing Flowers charges $125 plus $60 for each standard floral arrangement to deliver and set up
flowers for a banquet. (a) Write an equation inslope-intercept form that shows the cost for flowers for
any number of arrangements. (b) Find the cost of providing 20 floral arrangements.
58. A person weighing 150 pounds burns about 320 Calories per hour walking at a moderate pace. Suppose
that the same person burns an average of 1500 Calories per day through basic activities. The total
Calories burned by that person can be represented by a linearequation. Find the particular equation in
the general form.
59. Renata González wants to increase the energy efficiency of her house by adding to the insulation
previously installed. The better material protects against heat loss, the higher its R-value, or resistance
to heat flow. A 1in coat has an R-value of 3.2, while 3in has 9.6 as well. (a) Write an equation in slopeintercept form that showsthe total R-value in the attic if she adds x number of inches of additional
insulation. (b) Estimate the total R-value in the attic if she adds 6 inches of insulation.
60. The value of an automobile that has 6 years of use is $42,000, but 3 years ago, it was 96,000. If the
value of the automobile varies linearly with the time: (a) Find an equation relating the value of the
automobile at t...