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Calculus Quiz Days 5-7 > Study > Flashcards

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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
log(a)A - log(a)B equals
log(a)A/B
26
log(a)A^c equals
c log(a)A
27
c log(a)A
log(a)A^c
28
Change of base formula
log(b)x = log(a)x/log(a)b
29
log(b)x = log(a)x/log(a)b
Change of base formula
30
To graph a function like this: y=-2(x-3)^1 (x+1)^3 (x+4)^1 What is done?
Add of exponents and consider negative sign in front. It will be similar to the graph of -x^5 but with curved points
31
How do you graph this function?: y=3-2 √4-x
Plug in three numbers for x that make the radical square-root-able and gets u values
32
For a composite function (f o g), the domain is
Defined when both f(x) and f(g(x)) are defined.
33
Defined when both f(x) and f(g(x)) are defined.
For a composite function (f o g)
34
How would you prove (f o g)(x) = (g o f)(x)?
Find domains of each and compare.
35
What does [cos(x+9)]^2 equal?
cos^2(x+9)
36
What does cos^2(x+9) equal?
[cos(x+9)]^2
37
What is the graph of 1/x^2 like?
Two hyperbolas one in quadrant 1 and one in quadrant 2
38
Two hyperbolas one in quadrant 1 and one in quadrant 2
Graph of 1/x^2
39
Find vertical asymptotes of a function
Set denominator equal to zero
40
Set denominator equal to zero
Find vertical asymptotes of a function
41
How to find x values of: y=log(3)(x-1) + 2
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
How do you graph: y=(1/3)^x
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
b^(x+y) equals
b^x • b^y
44
b^x • b^y equals
b^(x+y)
45
b^(x-y) equals
b^x / b^y
46
b^x / b^y equals
b^(x-y)
47
(ab)^x equals
a^x • b^x
48
a^x • b^x equals
(ab)^x
49
Horizontal line test can test what type of function?
One-to-one
50
How to tell if the graph if a function is one-to-one?
Horizontal line test
51
How is an inverse function defined?
f(x) = y <=> f^-1(y) = x
52
f(x) = y <=> f^-1(y) = x
Definition of inverse function
53
What do f(f^-1(x)) and f^-1(f(x)) equal?
x
54
How is log(2)(16) evaluated?
Have to find number common with base so: log(2)(2^4) = 4log(2)(2) = 4
55
What does y=ln(x) equal?
e^y=x
56
What does e^y=x equal?
y=ln(x)
57
Change of base formula (natural logs)
log(b)(x)=ln(x) / ln(b)
58
log(b)(x)=ln(x) / ln(b)
Change of base formula (natural logs)
59
How do you evaluate log(8)(5)?
Change of base formula: log(8)(5)= ln(5) / ln(8)
60
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?
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
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).
Expressing area of a rectangle in terms of the length of one of its sides.
62
What is the domain of the area of a rectangle as a function of length when assuming width < length?
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
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.
Domain of the area of a rectangle as a function of length when assuming width < length.
64
Area and domain of an equilateral triangle.
A(x)= √3/4(x^2) where the domain is (0, ∞) because a side cannot be negative.
65
A(x)= √3/4(x^2) where the domain is (0, ∞) because a side cannot be negative.
Area and domain of an equilateral triangle
66
What happens when you get the number √2/7 where the whole thing is square rooted?
It also means √2/√7 so rationalize by multiplying by √7 to get √14(over)7
67
Order of transformations
``` H-shift H-stretch/shrink Reflect y-axis Vert-stretch/shrink Reflect x-axis Vert-shift ```
68
``` H-shift H-stretch/shrink Reflect y-axis Vert-stretch/shrink Reflect x-axis Vert-shift ```
Order of transformations
69
How do you reflect the graph of y=e^x over the line y=7 and x=3?
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
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.
Reflecting graphs over y lines and x lines

Calculus Quiz Days 5-7 (1 decks)

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