Let’s solve the problems step-by-step based on the uploaded image.

Problem 1: $f(x) = 3^x$

(a) Write down the value of $f(4)$ and $f(-1)$:

1. $f(4) = 3^4 = 81$
2. $f(-1) = 3^{-1} = \frac{1}{3}$

(b) Find the value of $k$ such that $f(x + 2) = kf(x)$ ($k$ is an integer):

Using the given function $f(x) = 3^x$: $f(x + 2) = 3^{x + 2} = 3^x \cdot 3^2 = 9 \cdot 3^x$ This implies $k = 9$.

Problem 2: $g(x) = \log_3(x + 2) - 2$

(a) Find the domain and range:

1. Domain: The argument of the logarithm, $x + 2$, must be positive: $x + 2 > 0 \implies x > -2$ Hence, the domain is $(-2, \infty)$.

2. Range: Since $\log_3(x + 2)$ has a range of $(-\infty, \infty)$, subtracting 2 does not affect the range. The range remains $(-\infty, \infty)$.