Question

graphing question on behalf of @Nicole

Answer 1

graphing is the easy part, we just have to move all the points up 1 and right 3

Answer 2

re-writing the function is a bit more difficult

translating up and down: you just have to add/ subtract the desired amount from the whole equation, so translating up 1 is just adding 1 to the entire equation

y = 3 * 2^x + 1
(the 1 is not part of the exponent)

to translate to the right, we subtract 3 from x (not from the whole function, just x)

so y = 3 *2^(x-3) + 1

Answer 3

so the new function is y = 3 *2^(x-3) + 1

Answer 4

yes

Answer 5

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Answer 6

similar process as before

1) translate down 5 units --> subtract 5 from the entire function
2) left two units --> add 2 to x only

can you try applying this to y = (0.5)^x ?

Answer 7

so i just need to add 2 to x to find the new funtion?: y = (0.5)^x

Answer 8

gotta remember both steps
1. subtract 5 from the whole function
2. add 2 to the x part only

Answer 9

y = (0.5)^x-5

Answer 10

im confused a bit loll

Answer 11

you're almost there

if we want to just add 2 to the x part we put x in parentheses and add 2

so y = (0.5)^(x+2)-5 should account for both transformations

Answer 12

got it, and how would the graph look?

Answer 13

well we kinda just do what the words say

"translate down 5 and left 2" so we just take all the points and move them down 5 and left 2

Answer 14

you just wanna identify any obvious points on the original graph (like 0,1 in the previous example), move down 5, 2 left, and draw the new point

Answer 15

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Answer 16

dilation by 2: multiply the entire function by 2 (so basically just write 2* in front)
a reflection across the x-axis --> add a negative sign in front of the equation

so what do you think might be the final result from this?

Answer 17

wdym "a reflection across the x-axis" like where would that be in the function?

Answer 18

if you look at the original problem it calls for "a reflection about the x-axis" which basically means the function gets "flipped" using the x-axis as a mirror (I can try drawing it)

Answer 19

to accomplish this we just need to multiply the entire function by -1

y = (1/4)^x becomes
y = -(1/4)^x

Answer 20

then the second part, dilating by 2, we just multiply the entire function by 2

so the end result is y = -2(1/4)^x

Answer 21

now, to draw this, we want to

1) draw the mirror image of the original function across the x-axis
and
2) dilate by 2 (make the curved part a bit steeper)

Answer 22

Oh okay that looks accurate enough

http://prntscr.com/lkhlxe

one more after this^

Answer 23

so to reflect across the y-axis we multiply x (just the x part) by -1
dilation of 1/2 --> multiply the entire function by 1/2

so applying these two operations to y = 4^x what do you think we get?

Answer 24

y = 4^x*(-1)

Answer 25

1. multiply the x by -1 ---> y = 4^(-x)
2. multiply the entire function by 1/2 ---> y = (1/2) * 4^(-x) --> end result

Answer 26

ohh ok

Answer 27

so if you just want to perform an operation on x it's a good idea to separate x into parentheses to keep it separate from the whole function

Answer 28

anyway to graph this just flip the function across the y-axis, then to dilate by 1/2 we make it less steep

Answer 29

still there?

Answer 30

yes sorry im here

Answer 31

but got that part

Answer 32

last one:

http://prntscr.com/lkhqih

Answer 33

ah

well in that case you just have to pick two things to do to the graph

so, like, you can translate up 3 and reflect across the x-axis (just an example), remember how to do that?

Answer 34

can you tell me one more time?

Answer 35

would recommend studying this chart on your own time

but translating up 3 ---> add 3 to the entire function
reflect across x-axis --> multiply the entire function by -1

Answer 36

Ugh this is confusing lmao

Answer 37

im sorry im literally just not in the mood for math but im trying to understand it loll

Answer 38

> if we want to reflect across the x-axis, multiply the function by -1

so y = 2 * 3^x ---> becomes y = -2 * 3^x

> if we want to translate a function up 3 units we add 3 to the function

so y = -2 * 3^x ---> becomes y = -2 * 3^x + 3 as the end result of applying both transformations

Answer 39

then to graph you would just reflect the function across the x-axis (pretend the x-axis is a mirror and draw what the mirror image would be) then move all the points on the graph 3 units up

Answer 40

Got it, how about a and b?

Answer 41

the rules for these transformations have to be studied/memorized

a) is asking for the function we created y = -2 * 3^x + 3
b) is asking to graph the function we created (see the purple line)

Answer 42

okay thank you voca! illmake sure to study them