Question

describe the domain and range of $y = 3(6)^{x-1} - 8$.
the domain is ______ and the range is ______.
all real numbers, $x > 1$, $x > -8$, $x > 6$, $x > 3$, $y > 1$, $y > -8$, $y > 6$, $y > -1$

Explanation:

Step1: Identify domain of exponential function

For any exponential function of the form $a(b)^{x-h}+k$, there are no restrictions on the input $x$ (no values of $x$ make the function undefined).

Step2: Analyze range of the function

First, note that $6^{x-1} > 0$ for all real $x$. Multiply by 3: $3(6)^{x-1} > 0$. Subtract 8: $3(6)^{x-1} - 8 > -8$.

Answer:

The domain is all real numbers and the range is $y > -8$