Question

The graph shows f(x) and its transformationg (x)

Which equation correctly modelsg (x)?
g(x) = 3^x-7 – 2
g (x) = 3^x+7 - 2
g(x) = 3^x+2 - 7
g(x) = 3^x-2-7

Answer 1

`g(x) = {3}^(x - 2) - 7`

Explanation:

As we can see, the graph of transformation of f(x) is translated to the right and down.

then, g(x) = f(x - a) - b, where a & b > 0.

from the options, there are 4 translated function of f(x).

but on the second option

`{3}^(x + 7) - 2 = {3}^(x - ( - 7)) - 2`

a < 0, then it's not the answer we need, same as third option that makes only first and fourth left.

from the picture, horizontal asymptote of f(x) is y = 0.

on g(x) horizontal asymptote is y = -b, where -10 < -b < -5.

and from the options that are left, we can see only fourth option that satisfies what we need.