Brainscape's Knowledge GenomeTM


Top Flashcards (Certified)
All Flashcards

MATH 112 > MATH 112 Exam 1 Memorization > Flashcards

MATH 112 Exam 1 Memorization Flashcards

1
Q

(a/b)x =

A

ax/bx

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

Domain and range of y = x3

A
  • Domain: (-infinity, infinity)
  • Range: (-infinity, infinity)
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

What is one important prerequisite for a function to have an inverse function?

A

ONE-TO-ONE

(i.e., only one x-value for each y-value)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

Intermediate Value Theorem

A

The intermediate value theorem states that if f is a continuous function whose domain contains the interval [a, b], then it takes on any given value between f(a) and f(b) at some point within the interval.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

Domain and range of y = mx + b

A
  • Domain: (-infinity, infinity)
  • Range: (-infinity, infinity)
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

When x < 0

1/x =

A
  • sqrt 1/x2
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

When is it no helpful to multiply by the radical conjugate when evaluating limits?

A

When you are evaluating limits at infinity. Instead, you should divide by 1/xa where “a” is the greatest factor.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q
A

b

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q
A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

Domain and range of y = lxl

A
  • Domain: (-infinity, infinity)
  • Range: [0, infinity)
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

Log Base conversion:

loga x =

A

(logb x) / (logb a)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

Definition of Continuity

A
  • f(x) is continuous at x = a
  • limit as x approaches a of f(x) exists (this means
  • left limit must exist, right limit must exist, and they must be equal
  • f(a) exists (i.e., a is in the domain; i.e., there is a y-value for it; i.e., it is defined)

In short, the limit as x approaches a for f(x) = f(a) – [and they both exist]

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

loga (m) - loga (n) =

A

loga (m/n)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

ax • ay =

A

ax+y

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

sin(2x) = ?

A

2 sin x cos x

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

Limit Laws (and when they are true)

A

These laws do NOT apply when the limits do not exist! This includes when the limits are INFINITE! Infinite limits do not “exist”!!

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

tan(-x) = ?

A

tan x

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

45-45-90 Triangle

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

(when b<0 and n is even)

A

|b|

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

Domain and range of arctan x

A
  • Domain: (-infinity, infinity)
  • Range: (-π/2, π/2)
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

How to convert degrees to radians.

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

loga (m) + loga (n) =

A

loga (mn)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q
A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

Domain and range of y = x2

A
  • Domain: (-infinity, infinity)
  • Range: [0, infinity)
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
25
Q

When does the direct substitution property apply?

A

When a function is continuous!

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
26
Q

Squeeze Theorem

A

NOTE: The functions do NOT have to be continuous!

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
27
Q

How to convert radians to degrees

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
28
Q

Domain and range of tan x

A
  • Domain: π/2 + πn for all integers n
  • Range: (-infinity, infinity)
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
29
Q

y = bx when b < 1

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
30
Q

Domain and range of arccos x

A
  • Domain: [-1, 1]
  • Range: [0, π]
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
31
Q

y = bx when b < 0

A

b CANNOT BE NEGATIVE

32
Q

Things you can’t do with radicals…

33
Q

Do infinite limits “exist?”

34
Q

sin2 x + cos2 x = ?

35
Q

(when b is non-zero and n>1)

36
Q

cos(-x) = ?

37
Q

Domain and range of y = 1/x

A
  • Domain: (-infinity, 0) U (0, infinity)
  • Range: (-infinity, 0) U (0, infinity)
38
Q

sin(-x) = ?

39
Q

loga (a) =

40
Q

Domain and range of cos x

A
  • Domain: (-infinity, infinity)
  • Range: [-1, 1]
41
Q

Domain and range of sin x

A
  • Domain: (-infinity, infinity)
  • Range: [-1, 1]
42
Q

Domain and range of y = ex

A
  • Domain: (-infinity, infinity)
  • Range: (0, infinity)
43
Q

(a2b)3 =

44
Q

Domain and range of y = sqrt x

A
  • Domain: [0, infinity)
  • Range: [0, infinity)
45
Q

loga (1) =

47
Q

loga (m)n =

A

n loga (m)

48
Q

y = bx when b > 1

49
Q

n loga (m) =

50
Q

Which functions are continuous on their domains?

51
Q

Domain and range of ln x or log x

A
  • Domain: (0, infinity)
  • Range: (-infinity, infinity)
52
Q

a-x =

53
Q

Which functions have horizontal asymptotes (and where are they)?

A
  • 1/x has H.A. at y = 0
  • ex has H.A. at y = 0
  • arctan x has H.A. at y = -pi/2 and y = pi/2
54
Q

10log x =

55
Q

When x > 0

1/x = ?

56
Q

30-60-90 Triangle

57
Q

Domain and range of arcsin x

A
  • Domain: [-1, 1]
  • Range: [-π/2, π/2]
58
Q

(ax)y =

59
Q

ax / ay =

MATH 112 (4 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2025 Bold Learning Solutions. Terms and Conditions