Question

the table gives selected values of \\(k(x)\\), which is a continuous unrestricted exponential function.

\\(\

$$\begin{array}{|c|c|c|c|c|c|} \\hline x & -1 & 0 & 1 & 2 & 3 \\\\ \\hline k(x) & -73 & -35 & -16 & -6.5 & -1.75 \\\\ \\hline \\end{array}$$

\\)

what are the domain and range of the function?

• the domain is \\(x > 0\\), and the range is \\(k(x) < 0\\).
• the domain is \\(x < 0\\), and the range is \\(k(x) > 0\\).
• the domain is \\(-\infty < x < \infty\\), and the range is \\(k(x) < 0\\).
• the domain is \\(-\infty < x < \infty\\), and the range is \\(k(x) > 0\\).

Explanation:

Determine the domain of the function

The problem states that \(k(x)\) is a continuous unrestricted exponential function.
For any unrestricted exponential function, the domain is all real numbers.

$$ -\infty < x < \infty $$

Determine the range of the function

Using the Exponential Range knowledge point

$$
LATEXBLOCK0
$$

Match with the correct option

Comparing the domain and range to the choices:

• Domain: \(-\infty < x < \infty\)
• Range: \(k(x) < 0\)

This corresponds to the third option.

Answer:

• The domain is \(x > 0\), and the range is \(k(x) < 0\).
• The domain is \(x < 0\), and the range is \(k(x) > 0\).
• The domain is \(-\infty < x < \infty\), and the range is \(k(x) < 0\). (Correct answer)
• The domain is \(-\infty < x < \infty\), and the range is \(k(x) > 0\).