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:

Determine the equation of the reflected function

$$ g(x) = -f(x) = -\frac{1}{2}(2.5)^x $$

Analyze the range of the reflected function

$$
LATEXBLOCK0
$$

Match with the given options

$$ \text{Range: all real numbers less than 0} $$

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