Question

identify the key features of the function from the table.

\

$$\begin{array}{|c|c|} \\hline x & f(x) \\\\ \\hline -2 & 9 \\\\ \\hline -1 & 3 \\\\ \\hline 0 & 1 \\\\ \\hline 1 & \\frac{1}{3} \\\\ \\hline 2 & \\frac{1}{9} \\\\ \\hline \\end{array}$$

as x approaches positive infinity, f(x) approaches negative infinity.
as x approaches negative infinity, f(x) approaches positive infinity.
a = 1
b = 1
the function is increasing
the function is decreasing
a = \frac{1}{3}
b = \frac{1}{3}

Explanation:

Identify the exponential function form

$$ f(x) = a \cdot b^x $$

Determine the parameters a and b

$$
LATEXBLOCK0
$$

Analyze key features and end behavior

$$
LATEXBLOCK1
$$

Answer:

• As x approaches positive infinity, f(x) approaches negative infinity.
• As x approaches negative infinity, f(x) approaches positive infinity. (Correct answer)
• a = 1 (Correct answer)
• b = 1
• The function is increasing
• The function is decreasing (Correct answer)
• a = \frac{1}{3}
• b = \frac{1}{3} (Correct answer)