Question

which is the range of the function \\(f(x) = \frac{1}{7}(9)^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:

Analyze the base function

$$ 9^x > 0 \quad \text{for all } x \in \mathbb{R} $$

Apply the scalar multiplication

$$ f(x) = \frac{1}{7}(9)^x > 0 \quad \text{for all } x \in \mathbb{R} $$

Determine the range

$$ \text{Range: } (0, \infty) \implies \text{all real numbers greater than 0} $$

Answer:

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