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@Vocaloid
the inverse of a graph should be reflected about the y=x axis
any guesses?
C?
close, it's the other one, A :)
okay got it
@photonics
@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
can you walk me thru it please?
g(1) means plug in x = 1 into g(x) so g(x) = 2x - 3 = 2(1) - 3 = ?
because I see f(g) but not f(x)
1
I got 1 as my answer
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
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 = ?
B
good
so switch y and x, then re-solve for y basically x = (4/3)y then solve for y
B
good
yea good
good
good
be careful w/ question 7, x^3 / x is x^2 not x^3
question 8 is correct
oh its b my bad
the y-axis is the straight vertical line that splits the graph into left and right halves
U
good
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
0,4
good but there's one more point
2,0 i thinkk
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)
any ideas? how many units left and down do we go?
* from the origin
B
good
any ideas? notice how x = -1 has two different assigned values -3 and 1
hmm im not that sure I usually dont know how to answer these questions
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
okay getting it slowly
any ideas? do any of the x values match w/ multiple y's?
this is not a function
hm not quite since each x only connects to one y-value this is both a function + a relation
Oh I got mixed up
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
Its a function
good so both function + relation
any ideas? as a hint, at each time you can only have one distance traveled
A function only?
generally all functions are relations so both
any ideas? as a hint the y-value is just the x value times 5
C?
good
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?
D?
not quite, the intercept is positive 3 not negative 3 so C is the better option
the y-axis is the one that goes vertical/up and down
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?
C
be careful, "time of day" is not one of the variables the dependent variable to complete the walk (A)
dependent is usually y, just gotta know this
oh okay good 2 know
so its going to be B
yes
domain is x so just list all the x-values and stick them in brackets
B
good, B
not quite, range would be the f(x) column
its D
or B
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
Ohhh okay
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
C?
yup good 5
similar logic , find x = 2 and find the matching function value
B
good
just gotta plug in x = 5 into (1/3)(5 - 4x) be careful w/ order of operations.
D
good
C?
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?
B
good
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any ideas? as a hint these are the same points that were on the last question
B
good
just gotta add them together x + 11 + x - 7 = ?
C
good
we subtract them this time, taking care of signs 10x + 2 - (-8x + 5) = ?
C again
good
I know im tiring you almost done I appreciate it
2x^3 * (x^2 + 6x) = ? be careful w/ exponents and parentheses
D
yup good
divide this time 5x^6 / (15 x^(-2)) = ?
hmm A or C not sure
A i think
yup, A since 6 - (-2) = 8
A?
yup
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the trick for these is to draw the line y = x and reflect across that |dw:1535919722031:dw|
|dw:1535919729214:dw| so something like that purple line should be the inverse
so C
the inverse still has to cross (1,1) so this one is a better choice |dw:1535919874640:dw|
Ohh okay
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 = ?
A because it then equals 8x+1
good
B?
not quite. first we swap the x and y to get x = 5y + 6 then solve for y
A
good
one more after this
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
"before he started" a.k.a month 0 how much did have at month 0?
100
good so 100 = your solution
I got 1 wrong Thanks soooo much tho Voca
huh. interesting. idk why it wouldn't be a function though
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