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Calculus Quiz Days 5-7 > Study > Flashcards

Study Flashcards

1
Q

Even functions are symmetric with respect to

A

y-axis

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2
Q

Symmetric with respect to y-axis

A

Even function

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3
Q

Odd functions are symmetric with respect to

A

origin

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4
Q

Symmetric with respect to the origin

A

Odd function

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5
Q

A function is not a polynomial when

A

Power is not an integer

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6
Q

When a power is not an integer in a polynomial

A

It is not a polynomial

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7
Q

What is the domain of tanx?

A

{x € R | x ≠ π/2 + nπ}

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8
Q

{x € R | x ≠ π/2 + nπ}

A

Domain of tanx

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9
Q

How do you prove a function is odd?

A

Place (-x) in for x

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10
Q

Place (-x) in place of x to

A

Prove a function is odd

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11
Q

Constants are what type of function

A

Even

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12
Q

Can even functions be constants?

A

Yes

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13
Q

Functions that are not even or odd are not symmetric across

A

y-axis OR origin

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14
Q

Not symmetric across y-axis OR origin

A

Functions that are neither even nor odd

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15
Q

Rules of graphing inverse of a function

A

Reflect original over line y=x and any point (a,b) on f(x) equals
(b, a) on f^-1(x)

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16
Q

Reflect original over line y=x and any point (a,b) on f(x) equals
(b, a) on f^-1(x)

A

Rules of graphing inverse of a function

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17
Q

y = log(a)x equals

A

a^y = x

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18
Q

a^y = x equals

A

log(a)x

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19
Q

Every log function hits the point what on graph

A

(1, 0)

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20
Q

Always hits point (1,0) on graph

A

Log functions

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21
Q

What is the second point on the graph of log(5)x and why?

A

(5,1) because the base is five, and 5^1 equals 5. So the second five is the x and y is what it is raised to

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22
Q

log(a)AB equals

A

log(a)A + log(a)B

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23
Q

log(a)A + log(a)B equals

A

log(a)AB

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24
Q

log(a)A/B equals

A

log(a)A - log(a)B

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25
Q

log(a)A - log(a)B equals

A

log(a)A/B

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26
Q

log(a)A^c equals

A

c log(a)A

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27
Q

c log(a)A

A

log(a)A^c

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28
Q

Change of base formula

A

log(b)x = log(a)x/log(a)b

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29
Q

log(b)x = log(a)x/log(a)b

A

Change of base formula

30
Q

To graph a function like this:

y=-2(x-3)^1 (x+1)^3 (x+4)^1

What is done?

A

Add of exponents and consider negative sign in front. It will be similar to the graph of -x^5 but with curved points

31
Q

How do you graph this function?:

y=3-2 √4-x

A

Plug in three numbers for x that make the radical square-root-able and gets u values

32
Q

For a composite function (f o g), the domain is

A

Defined when both f(x) and f(g(x)) are defined.

33
Q

Defined when both f(x) and f(g(x)) are defined.

A

For a composite function (f o g)

34
Q

How would you prove (f o g)(x) = (g o f)(x)?

A

Find domains of each and compare.

35
Q

What does [cos(x+9)]^2 equal?

A

cos^2(x+9)

36
Q

What does cos^2(x+9) equal?

A

[cos(x+9)]^2

37
Q

What is the graph of 1/x^2 like?

A

Two hyperbolas one in quadrant 1 and one in quadrant 2

38
Q

Two hyperbolas one in quadrant 1 and one in quadrant 2

A

Graph of 1/x^2

39
Q

Find vertical asymptotes of a function

A

Set denominator equal to zero

40
Q

Set denominator equal to zero

A

Find vertical asymptotes of a function

41
Q

How to find x values of:

y=log(3)(x-1) + 2

A

Use inside of parentheses:

x-1 = 0 (vertical asymptote)
x-1 = 1 (first x value)
x-1 = 3 (base)

Plug these in to original function to find y values

42
Q

How do you graph:

y=(1/3)^x

A

Know that this equals y=3^-x:

  • x=0=0 (y-intercept)
  • x=-=-1 (second point)

So, points at (0,1) and (-1,3)

43
Q

b^(x+y) equals

A

b^x • b^y

44
Q

b^x • b^y equals

A

b^(x+y)

45
Q

b^(x-y) equals

A

b^x / b^y

46
Q

b^x / b^y equals

A

b^(x-y)

47
Q

(ab)^x equals

A

a^x • b^x

48
Q

a^x • b^x equals

A

(ab)^x

49
Q

Horizontal line test can test what type of function?

A

One-to-one

50
Q

How to tell if the graph if a function is one-to-one?

A

Horizontal line test

51
Q

How is an inverse function defined?

A

f(x) = y <=> f^-1(y) = x

52
Q

f(x) = y <=> f^-1(y) = x

A

Definition of inverse function

53
Q

What do f(f^-1(x)) and f^-1(f(x)) equal?

A

x

54
Q

How is log(2)(16) evaluated?

A

Have to find number common with base so:

log(2)(2^4) = 4log(2)(2) = 4

55
Q

What does y=ln(x) equal?

A

e^y=x

56
Q

What does e^y=x equal?

A

y=ln(x)

57
Q

Change of base formula (natural logs)

A

log(b)(x)=ln(x) / ln(b)

58
Q

log(b)(x)=ln(x) / ln(b)

A

Change of base formula (natural logs)

59
Q

How do you evaluate log(8)(5)?

A

Change of base formula:

log(8)(5)= ln(5) / ln(8)

60
Q

If a rectangle has a perimeter of 24 ft and you need to find a function that models its area A in terms of the length L of one of its sides, what do you do?

A

Make L the only variable:

P=2L+2w and since
P=24, that means 24=2L+2w and w=12-L.
Since A=Lw, this means A(L)=L(12-L).

61
Q

Make L the only variable:

P=2L+2w and since
P=24, that means 24=2L+2w and w=12-L.
Since A=Lw, this means A(L)=L(12-L).

A

Expressing area of a rectangle in terms of the length of one of its sides.

62
Q

What is the domain of the area of a rectangle as a function of length when assuming width < length?

A

Let A(L)=L(12-L). The domain would be (6,12) because if L=6, width would be 6. If L=12, width would be 0.

63
Q

Let A(L)=L(12-L). The domain would be (6,12) because if L=6, width would be 6. If L=12, width would be 0.

A

Domain of the area of a rectangle as a function of length when assuming width < length.

64
Q

Area and domain of an equilateral triangle.

A

A(x)= √3/4(x^2) where the domain is (0, ∞) because a side cannot be negative.

65
Q

A(x)= √3/4(x^2) where the domain is (0, ∞) because a side cannot be negative.

A

Area and domain of an equilateral triangle

66
Q

What happens when you get the number √2/7 where the whole thing is square rooted?

A

It also means √2/√7 so rationalize by multiplying by √7 to get √14(over)7

67
Q

Order of transformations

A 
H-shift
H-stretch/shrink
Reflect y-axis
Vert-stretch/shrink
Reflect x-axis
Vert-shift
68
Q 
H-shift
H-stretch/shrink
Reflect y-axis
Vert-stretch/shrink
Reflect x-axis
Vert-shift
A

Order of transformations

69
Q

How do you reflect the graph of y=e^x over the line y=7 and x=3?

A

For y-values, add negative to coefficient and add double the y-value. For x-values, add negative to x and add double the x-value to x.

70
Q

For y-values, add negative to coefficient and add double the y-value. For x-values, add negative to x and add double the x-value to x.

A

Reflecting graphs over y lines and x lines

Calculus Quiz Days 5-7 (1 decks)

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