Question

can someone help me graph this step by step?

Answer 1

you can plug in various x values to get corresponding y values. Then you plot each (x,y) point and draw a curve through all the points

or you can use technology like a graphing calculator. If you don't have a graphing calculator, you can use this

https://www.desmos.com/calculator

Answer 2

so there's really no like specific way in doing it, plugging in points is fine?

Answer 3

yeah it varies depending on the equation, but the basics are still the same

Answer 4

for example, if you plug in x = 0 you should get y = 5

so (0,5) is on the curve

Answer 5

okay, thanks!

Answer 6

here is what desmos is saying
https://www.desmos.com/calculator/skbgnnyg55

Answer 7

I provided the table to allow you to play with it and add other x values (so it will compute the corresponding y values)

to figure out the range, I suggest you plug in large x values that get larger and larger so you can see what's going on with y

Answer 8

thanks!! and do you know if this type of equation contains asymptotes?

Answer 9

hmm for some reason, it glitches

Answer 10

I plugged in x = 100 and got y = 2 which is misleading

Answer 11

y = 2 is the horizontal asymptote

the curve slowly approaches this horizontal line but never touches it

Answer 12

so that's why the range is y > 2

Answer 13

how do you find the asymptotes ?

Answer 14

well if you use a calculator, and plug in some large x number like x = 20, you will get

3*(1/3)^x = 3*(1/3)^20= 0.0000000008604

so the asymptote for 3*(1/3)^x is y = 0
it gets closer and closer to 0, but never gets there

Answer 15

the +2 at the end moves the asymptote up 2 units

Answer 16

notice how 3*(1/3)^25 = 0.00000000000354 which is even smaller, so that confirms things are getting smaller

Answer 17

one last question, how do you know if the +2 is h or k?

Answer 18

it's k

Answer 19

3(1/3)^x + 2 is in the form a(b)^(x-h) + k where

a = 3
b = 1/3
h = 0
k = 2

Answer 20

okay thanks!!!

Answer 21

h shifts things left and right
k shifts things up and down

Answer 22

got it! thanks so much (: