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:

Step1: Analyze the exponential term

The term $9^x$ is an exponential function with base $9>1$. For all real $x$, $9^x > 0$.

Step2: Apply the scalar multiplier

Multiply by $\frac{1}{7}$: $\frac{1}{7} \times 9^x > \frac{1}{7} \times 0$, so $f(x) > 0$.

Step3: Define the range

The output values of $f(x)$ are all positive real numbers.

Answer:

all real numbers greater than 0