Question

ain, range, and evaluate exponential function
z.1 domain and range of exponential functions efd
what is the range of this exponential function?
$y = \frac{1}{3} \cdot 10^{x + 4}$
$\\{y \mid y \geq 0\\}$
$\\{y \mid y > 0\\}$
all real numbers
$\\{y \mid y < 0\\}$
$\\{y \mid y \leq 0\\}$

Explanation:

Step1: Analyze base exponential term

The term $10^x$ is a standard exponential function. For all real $x$, $10^x > 0$.

Step2: Apply vertical transformation

Multiply by $\frac{1}{3}$: $\frac{1}{3} \cdot 10^x > 0$, since multiplying a positive value by a positive constant preserves positivity.

Step3: Apply vertical shift

Add 4: $\frac{1}{3} \cdot 10^x + 4 > 0 + 4$, so $\frac{1}{3} \cdot 10^x + 4 > 0$. All resulting values of $y$ are positive.

Answer:

$\{y \mid y > 0\}$