2. Consider the function $f(x)=-\left(\frac{1}{3}\right)^{x+2}+4$, find the following:
e. The parent function
f. The vertical intercept of $f(x)$ written as an ordered pair
g. The equation of the horizontal asymptote
h. Sketch $f(x)$
Answer
\(\boxed{\text{The parent function is } f(x) = a^x. \text{ The vertical intercept of } f(x) \text{ is } (0, 4). \text{ The equation of the horizontal asymptote is } y = 4. \text{ The graph of } f(x) \text{ is a decreasing function that approaches the line } y = 4 \text{ as } x \text{ approaches infinity.}}\)
Step 1 ：The parent function is \(f(x) = a^x\).
Step 2 ：The vertical intercept of \(f(x)\) is the point \((0, f(0)) = (0, 4)\).
Step 3 ：The horizontal asymptote of \(f(x)\) is the line \(y = 4\).
Step 4 ：The graph of \(f(x)\) is a decreasing function that approaches the line \(y = 4\) as \(x\) approaches infinity.
Step 5 ：\(\boxed{\text{The parent function is } f(x) = a^x. \text{ The vertical intercept of } f(x) \text{ is } (0, 4). \text{ The equation of the horizontal asymptote is } y = 4. \text{ The graph of } f(x) \text{ is a decreasing function that approaches the line } y = 4 \text{ as } x \text{ approaches infinity.}}\)
