Question

the graph of (f(x) = \frac{1}{2}(2.5)^x) and its reflection across the x-axis, (g(x)), are shown.

what is the range of (g(x))?

• all real numbers
• all real numbers less than 0
• all real numbers greater than 0
• all real numbers less than or equal to 0

Explanation:

Identify the function and its transformation

$$
LATEXBLOCK0
$$

Determine the range of the transformed function

$$
LATEXBLOCK1
$$

Match with the given options

$$ \text{Range of } g(x) \text{ is } (-\infty, 0), \text{ which corresponds to "all real numbers less than 0".} $$

Answer:

• all real numbers
• all real numbers less than 0 (Correct answer)
• all real numbers greater than 0
• all real numbers less than or equal to 0