How to solve the equation of the new function, domain and range?

Question

The graph of f(x) = (1.68)^x is shifted right 3 units, stretched vertically by a factor of 2, reflected about the x-axis, and then shifted downward 3 units.

What is the equation of the new function, g(x)?

State its y-intercept (to the nearest thousandth), domain, and range.

Answer 1

One step at a time

We start with f(x) = 1.68^x

We shift right 3

1.68^(x-3)

stretch vertically by 2

2 * 1.68^(x-3)

reflect about the x axis

-2 * 1.68^(x-3)

down 3

-2 * 1.68^(x-3) - 3

The y intercept is

-2 * 1.68^-3 - 3 = -3.422

The domain is (-∞, ∞)

The range is (-∞, -3)