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Mathematics 13 Online
Nicole:

Question: http://prntscr.com/kprwyc Answer choices: http://prntscr.com/kprx41 http://prntscr.com/kprx6p http://prntscr.com/kprx9z http://prntscr.com/kprxdh

Nicole:

@Vocaloid

photonics:

the inverse of a graph should be reflected about the y=x axis

photonics:

any guesses?

Nicole:

C?

photonics:

close, it's the other one, A :)

Nicole:

okay got it

Nicole:

http://prntscr.com/kps2o0

Nicole:

@photonics

Nicole:

@Vocaloid

Vocaloid:

start from the inside of the parentheses and work your way out so find g(1) by plugging in x = 1 into 2x - 3 then take the result from that and plug that into 5x

Nicole:

can you walk me thru it please?

Vocaloid:

g(1) means plug in x = 1 into g(x) so g(x) = 2x - 3 = 2(1) - 3 = ?

Nicole:

because I see f(g) but not f(x)

Nicole:

1

Nicole:

I got 1 as my answer

Vocaloid:

check your signs again 2(1) - 3 = 2 - 3 which is -1 not 1 so g(1) = -1, we plug this into f(x) = 5x giving us f(g(1)) = -5 = your solution

Nicole:

http://prntscr.com/kps759

Vocaloid:

so we plug the entire expression for g(x) into the x for f(x) so f(x) = 3x + 2, then f(g(x)) = 3(x-5) + 2 = ?

Nicole:

B

Vocaloid:

good

Nicole:

http://prntscr.com/kps8ek

Vocaloid:

so switch y and x, then re-solve for y basically x = (4/3)y then solve for y

Nicole:

B

Vocaloid:

good

Nicole:

is this correct? http://prntscr.com/kpsava

Vocaloid:

yea good

Nicole:

http://prntscr.com/kpsb01

Vocaloid:

good

Nicole:

http://prntscr.com/kpsbq0

Vocaloid:

good

Nicole:

http://prntscr.com/kpsc11

Vocaloid:

be careful w/ question 7, x^3 / x is x^2 not x^3

Vocaloid:

question 8 is correct

Nicole:

oh its b my bad

Nicole:

http://prntscr.com/kpsczq

Vocaloid:

the y-axis is the straight vertical line that splits the graph into left and right halves

Nicole:

U

Vocaloid:

good

Nicole:

http://prntscr.com/kpsdev

Vocaloid:

so the trick for these is to reverse the coordinates and see which points are on the existing graph so reversed, the coordinates are (0,4) (2,0) (0,-2) (4,0) see which one(s) are on the existing graph

Nicole:

0,4

Vocaloid:

good but there's one more point

Nicole:

2,0 i thinkk

Vocaloid:

good so we reverse the coordinates again to get the actual answer so (4,0) and (0,2) are your solutions (the first two checkboxes)

Nicole:

http://prntscr.com/kpsfu7

Vocaloid:

any ideas? how many units left and down do we go?

Vocaloid:

* from the origin

Nicole:

B

Vocaloid:

good

Nicole:

http://prntscr.com/kpsg0n

Vocaloid:

any ideas? notice how x = -1 has two different assigned values -3 and 1

Nicole:

hmm im not that sure I usually dont know how to answer these questions

Vocaloid:

well to be a function, each x would only have 1 assigned value so it's not a function, but it ~is~ a relation so A would be the best solution

Nicole:

okay getting it slowly

Nicole:

http://prntscr.com/kpsgef

Vocaloid:

any ideas? do any of the x values match w/ multiple y's?

Nicole:

this is not a function

Vocaloid:

hm not quite since each x only connects to one y-value this is both a function + a relation

Nicole:

Oh I got mixed up

Nicole:

http://prntscr.com/kpsi33

Vocaloid:

so there's this thing called the vertical line test, if you can draw a vertical line somewhere that crosses the graph more than once, it's not a function otherwise its a function

Nicole:

Its a function

Vocaloid:

good so both function + relation

Nicole:

http://prntscr.com/kpsiv9

Vocaloid:

any ideas? as a hint, at each time you can only have one distance traveled

Nicole:

A function only?

Vocaloid:

generally all functions are relations so both

Nicole:

http://prntscr.com/kpsiyo

Vocaloid:

any ideas? as a hint the y-value is just the x value times 5

Nicole:

C?

Vocaloid:

good

Nicole:

http://prntscr.com/kpskkn

Vocaloid:

well y = mx + b is the general form where b is the y-intercept so since the y-intercept is 3 which one might be the best option?

Nicole:

D?

Vocaloid:

not quite, the intercept is positive 3 not negative 3 so C is the better option

Vocaloid:

the y-axis is the one that goes vertical/up and down

Nicole:

got it http://prntscr.com/kpsm9b

Vocaloid:

hm, so independent is the one that influences/determines the other, and the dependent is entirely dependent on the independent so that being said, does your speed determine the time or does the time spent walking determine the speed?

Nicole:

C

Vocaloid:

be careful, "time of day" is not one of the variables the dependent variable to complete the walk (A)

Nicole:

oh I went for the wrong one http://prntscr.com/kpsmxz

Vocaloid:

dependent is usually y, just gotta know this

Nicole:

oh okay good 2 know

Nicole:

so its going to be B

Vocaloid:

yes

Nicole:

http://prntscr.com/kpsnze

Vocaloid:

domain is x so just list all the x-values and stick them in brackets

Nicole:

B

Vocaloid:

good, B

Nicole:

http://prntscr.com/kpspdt

Vocaloid:

not quite, range would be the f(x) column

Nicole:

its D

Nicole:

or B

Vocaloid:

hm not quite, f(x) has the values 5, 10, 15, 25 so B is the better option usually we list the range values in order regardless of how they appear

Nicole:

Ohhh okay

Nicole:

http://prntscr.com/kpspj3

Vocaloid:

f(4) means the value of f(x) when x = 4 so go to x = 4 into the table and see what the f(x) value is

Nicole:

C?

Vocaloid:

yup good 5

Nicole:

http://prntscr.com/kpsqik

Vocaloid:

similar logic , find x = 2 and find the matching function value

Nicole:

B

Vocaloid:

good

Nicole:

http://prntscr.com/kpsqsn

Vocaloid:

just gotta plug in x = 5 into (1/3)(5 - 4x) be careful w/ order of operations.

Nicole:

D

Vocaloid:

good

Nicole:

Question: http://prntscr.com/kpss8z Answer Choices: http://prntscr.com/kpssdt

Nicole:

C?

Vocaloid:

hm not quite. c doesn't work b/c (-4,4) is not on the graph if we look at the graph we can see (-2,-5) and (-1,-2), right? so what might the best solution be?

Nicole:

B

Vocaloid:

good

Vocaloid:

any ideas? as a hint these are the same points that were on the last question

Nicole:

B

Vocaloid:

good

Nicole:

http://prntscr.com/kpstvf

Vocaloid:

just gotta add them together x + 11 + x - 7 = ?

Nicole:

C

Vocaloid:

good

Nicole:

http://prntscr.com/kpsuom

Vocaloid:

we subtract them this time, taking care of signs 10x + 2 - (-8x + 5) = ?

Nicole:

C again

Vocaloid:

good

Nicole:

http://prntscr.com/kpsv77

Nicole:

I know im tiring you almost done I appreciate it

Vocaloid:

2x^3 * (x^2 + 6x) = ? be careful w/ exponents and parentheses

Nicole:

D

Vocaloid:

yup good

Nicole:

http://prntscr.com/kpsvos

Vocaloid:

divide this time 5x^6 / (15 x^(-2)) = ?

Nicole:

hmm A or C not sure

Nicole:

A i think

Vocaloid:

yup, A since 6 - (-2) = 8

Nicole:

http://prntscr.com/kpswy8

Nicole:

A?

Vocaloid:

yup

Vocaloid:

the trick for these is to draw the line y = x and reflect across that |dw:1535919722031:dw|

Vocaloid:

|dw:1535919729214:dw| so something like that purple line should be the inverse

Nicole:

so C

Vocaloid:

the inverse still has to cross (1,1) so this one is a better choice |dw:1535919874640:dw|

Nicole:

Ohh okay

Nicole:

http://prntscr.com/kpsy57

Vocaloid:

this one requires a bit of calculation for each function we need to take the value of g(x) and plug it into the x-value of f(x) and see which one produces the desired result start w/ A f(x) = 2x + 3 g(x) = 4x - 1 f(g(x)) = 2(4x-1) + 3 = ?

Nicole:

A because it then equals 8x+1

Vocaloid:

good

Nicole:

http://prntscr.com/kpt0hs

Nicole:

B?

Vocaloid:

not quite. first we swap the x and y to get x = 5y + 6 then solve for y

Nicole:

A

Vocaloid:

good

Nicole:

http://prntscr.com/kpt16h

Nicole:

one more after this

Vocaloid:

this is a tricky question the function gives the amount of battery ~left~ not the amount of battery needed so none of these would be the best imo

Nicole:

Last one: http://prntscr.com/kpt27j

Vocaloid:

"before he started" a.k.a month 0 how much did have at month 0?

Nicole:

100

Vocaloid:

good so 100 = your solution

Nicole:

I got 1 wrong Thanks soooo much tho Voca

Nicole:

this is the question I got wrong: http://prntscr.com/kpt342

Vocaloid:

huh. interesting. idk why it wouldn't be a function though

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