Question

the graph of (f(x) = 6(0.25)^x) and its reflection across the y-axis, (g(x)), are shown.

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

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

Explanation:

Identify the function and transformation

$$ f(x) = 6(0.25)^x $$

$$ g(x) = f(-x) = 6(0.25)^{-x} $$

Determine the domain of the transformed function

$$ \text{Domain of } f(x): x \in \mathbb{R} $$

$$ \text{Domain of } g(x): -x \in \mathbb{R} \implies x \in \mathbb{R} $$

Match with the given options

$$ \text{Domain} = \text{all real numbers} $$

Answer:

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