Question

calc:

Answer 1

@jim_thompson5910 please work me through the steps- if you can

Answer 2

Let's first find f(-x)

\[\Large f(x) = x^{-4} + \cos(-2x)\]

\[\Large f(x) = \frac{1}{x^{4}} + \cos(2x)\]

\[\Large f(-x) = \frac{1}{(-x)^{4}} + \cos(2(-x))\]

\[\Large f(-x) = \frac{1}{x^4} + \cos(-2x)\]

\[\Large f(-x) = x^{-4} + \cos(-2x)\]

\[\Large f(-x) = f(x)\]

So that shows f(x) is at least even


Notes:
anything to an even power is positive (eg: (-2)^4 = 2^4)

Also, cos(-x) = cos(x)

Answer 3

with me so far?

Answer 4

yes!

Answer 5

Now let's find `-f(x)`


\[\Large f(x) = x^{-4} + \cos(-2x)\]
\[\Large -f(x) = -(x^{-4} + \cos(-2x))\]
\[\Large -f(x) = -x^{-4} - \cos(-2x)\]

Which is clearly different, so \[\Large f(-x) \ne -f(x)\]

meaning that f(x) is NOT odd

Answer 6

yeah it's even but not odd

Answer 7

I think the only case where a function is both even and odd is when f(x) = 0 for all x

Answer 8

@jim_thompson5910

Answer 9

do you recall how to find the slope of any line through 2 given points?

ie, do you remember the slope formula?

Answer 10

y=mx+b @jim_thompson5910

Answer 11

Slope Formula
\[\Large m = \frac{y_2 - y_1}{x_2 - x_1}\]

Answer 12

you wrote out slope intercept form

Answer 13

oops yeah !@jim_thompson5910

Answer 14

do you see what the y coordinates of the points are? if so, tell me what they are

Answer 15

hint: it's the second coordinate of each point

example: (5,7) has a y coordinate of 7

Answer 16

Use the slope formula to get...

\[\Large m = \frac{y_2 - y_1}{x_2 - x_1}\]
\[\Large m = \frac{0-(-2)}{12-9}\]
\[\Large m = \frac{0+2}{12-9}\]
\[\Large m = \frac{2}{3}\]

Then we use this slope and a point, say (12,0), to find the equation

y = mx + b
0 = (2/3)(12) + b
0 = 8 + b
b = -8

So the equation of this line in slope intercept form is \[\Large y = \frac{2}{3}x+8\]

Answer 17

@jim_thompson5910

Answer 18

math is more my specialty

Answer 19

sorry for some reason, I made a typo. Instead of \[\Large y = \frac{2}{3}x+8\] it should be \[\Large y = \frac{2}{3}x-8\]

Answer 20

g(x) = f(x-2) + 4


First let's find f(x-2). Replace every copy of x with (x-2)

f(x) = x^3 + 2
f(x-2) = (x-2)^3 + 2
f(x-2) = (x-2)*(x-2)^2 + 2
f(x-2) = (x-2)*(x^2-4x+4) + 2
f(x-2) = x*(x^2-4x+4)-2*(x^2-4x+4) + 2
f(x-2) = x^3-4x^2+4x-2x^2+8x-8 + 2
f(x-2) = x^3-4x^2-2x^2+4x+8x-8 + 2
f(x-2) = x^3-6x^2+12x-6



Now let's tack on a +4 at the end

f(x-2)+4 = x^3-6x^2+12x-6+4
f(x-2)+4 = x^3-6x^2+12x-2


So,
g(x) = x^3-6x^2+12x-2

Answer 21

I would use a graphing tool like desmos

https://www.desmos.com/calculator

and locate the highest and lowest points

Answer 22

could you show me how and work through it with me?? @jim_thompson5910

Answer 23

can you example?

Answer 24

what is the domain of y = cos(x) ? any ideas?

Answer 25

all real numbers?

Answer 26

yes, how about the range?

Answer 27

-1≤y≤1?

Answer 28

yep, now multiply all sides by 10 and you get what?

Answer 29

not sure... what you get>?

Answer 30

\[\Large -1 \le y \le 1\]
\[\Large 10(-1) \le 10*y \le 10*1\]
\[\Large -10 \le 10y \le 10\]


So the range of y = 10cos(x) is \(\Large -10 \le y \le 10\)

Answer 31

so then how would i find the maximum and minimum values ??

Answer 32

the min and max are based on the range I just wrote out

Answer 33

could i ask you an econ question real quick that is fairly easy?? @jim_thompson5910

Answer 34

I can't guarantee anything

Answer 35

its fine- just give it your best shot please:-) I think oysters and stopwatches so far but i have to pick another too

Answer 36

yep so far so good

Answer 37

think of another item you would see on store shelves

Answer 38

yes

Answer 39

ok... and what about this one?? thanks for realizing that with me!

Answer 40

you posted the same question twice

Answer 41

resource and firm sound right

Answer 42

resource and part of the circular flow maybe?

Answer 43

are you pretty sure on that? i think so too just want to be 100% sure...

Answer 44

no not 100%

Answer 45

which ones do you think?

Answer 46

choices B and D..?

Answer 47

autos are part of the product market, not factor

Answer 48

oops i meant B and E

Answer 49

yep

Answer 50

households offer labor because people that live in the houses offer to work for pay

households offer capital in the form of investing (eg stocks)

households also offer land. A landlord can rent out his/her land to a company to use

Answer 51

in summary: households offer land, labor and capital

Answer 52

so you would say A and D then right???

Answer 53

yes

Answer 54

I'm thinking D or E... so last 2 cup for grabs there is only 1 right answer

Answer 55

"monopsony" means "one buyer"

Answer 56

i know and I'm think either D or E .. thoughts?

Answer 57

D and E are very similar, but congress is not a single entity like the navy is. Congress is composed of 2 houses with 535 members total, plus other staff

Answer 58

ohhh so just the Navy then would be right??

Answer 59

besides, the term "Uniform" means "same" or "unified" in a sense. Which makes sense because the military all needs to be on the same page

Answer 60

oh ok- thanks!! I thought so but wasn't sure

Answer 61

im not so sure about this one....^

Answer 62

that would be revenue
revenue is the money flow of selling products and services (this is before taxes and expenses)

Answer 63

the answer i chose probably isnt even right

Answer 64

probably A but idk about this one

Answer 65

me neither... I'm not so sure

Answer 66

households, aka average everyday people

anyways I have to get going so have a good night

Answer 67

wait one more!! its last one i promise!