Question

Can someone please help me Find the Equation of this graph! (See Attachment)

Answer 1

dgjnevrenveinhhhuh... i know the y-int is 2, and the slope is -2...
what kind of line is that?.. i cant really put my finger on it..

Answer 2

do you have to work out its equation or are you given a set of equations to select from?

Answer 3

^ YEAH, that would help. xD

Answer 4

you need to pay attention to the key features of the curve

Answer 5

Nope i was given the graph and told to find the equation of the graph

Answer 6

1. It has a y-intercept of (0, 2)
2. It has an x-intercept of (1, 0)
3. It has a horizontal asymptote of y=-2

Answer 7

what type of methods have you been taught on this topic?

Answer 8

It's Exponential Functions and it didnt cover what to do in this situation

Answer 9

ah! ok - then it is most definitely not that - let me think again...

Answer 10

it should be some variation of this function:\[y=2e^{-x}\]see here: http://www.wolframalpha.com/input/?i=plot+2e^%28-x%29+for+x%3D-7+to+7+and+y%3D-7+to+7

Answer 11

can you give some examples of the types of exponential functions you have been told about?

Answer 12

f(x) = 5x - 1
f(x) = (1/5)x

Answer 13

those are not exponential functions

Answer 14

exponential functions involve e or log

Answer 15

i promise thats what it says...

Answer 16

then in all honesty i dont know what the heck is going on!

Answer 17

:)

Answer 18

Well Thanks for all your help! :) Seems like the questions are weird.. Thanks again :P

Answer 19

I'll keep thinking over it an reply here if I find anything useful.

Answer 20

ok I believe I have it!

Answer 21

if we let:\[y=a2^{-x}+b\]where a and b are constants, then we can use the intercepts to calculate them.
we know y=2 when x=0, so this gives:\[2=a+b\tag{1}\]we also know that y=0 when x=1, so this gives:\[0=a2^{-1}+b=\frac{a}{2}+b\implies b=-\frac{a}{2}\tag{2}\]substituting the expression for b from (2) into (1) we get:\[2=a-\frac{a}{2}=\frac{a}{2}\implies a=4\tag{3}\]substituting (3) into (2) gives:\[b=-\frac{4}{2}=-2\]thus:\[y=4\times2^{-x}-2=2^2\times2^{-x}-2=2^{2-x}-2\]see here: http://www.wolframalpha.com/input/?i=plot+2^%282-x%29+-+2+for+x%3D-7+to+7+and+y%3D-7+to+7

Answer 22

and we can also see that with this function, the limit as x tends to infinity of y will be -2, which matches your graph

Answer 23

Exponential Functions involve e, log or some number to the power of x.

Answer 24

I hope that all makes sense?

Answer 25

Yeah, Its making alot more sense now! Thanks!

Answer 26

yw :)