Question

Write the equation of an exponential function that has a y=-1 horizontal asymptote, a y-intercept of (0,-2) and passes through (2,15)

Answer 1

well just a thought at y intercept x component will be 0

In general an exponential function is of form \(a^x\) so wouldnt it be

y=\(a^x-3\)

Answer 2

1. horiz asymptote -> as x->inf, y=-1
2. when x=0, y=-2
3. when x=2, y=15

Answer 3

from 1, we know the exponential should be -ve.
and from 2, we know that y is shifted to left by 3 points->since a^0=1
\[y=a^{-x}-3\]
to find a, use the last point for x,y and find a

Answer 4

Judging by the two given points, you can infer that the function is increasing for the most part for positive values of x, and that the horizontal asymptote occurs as x approaches negative infinity:
\[\lim_{x\to-\infty}f(x)=-1\]

Answer 5

So the curve looks something like this: