Question

Write the function associated with the graph below

Answer 1

That's a positive slope... I don't know if that's the kind of answer you're looking for, but it's a start I guess.

Answer 2

Since the value of the function is decreasing exponentially as x decreases ,

The function is of the form
`y=ae^(bx)+c,b>0`.

Since the curve passes through (0,6),

`6=ae^(0)+c,6=a+c`,

Since the curve passes through (-1,0),

`0=ae^(-b)+c`.

Since
`y=-3` is a horizontal asymptote,

`-3=ae^(-\infty)+c,c=-3`

From the above 3 equations,

`c=-3,a=9,9e^(-b)=3,e^b=3,b=\ln 3`.

Therefore, the required function is

`image`.

It can be verified that the curve
`y=9*3^( x)-3` passes through
`(-2,-2)`.