what are the domain and range of the function f(x) = 3^x + 5?\no domain: (-∞,∞); range: (0,∞)\no domain…

Explanation:

Step1: Determine the domain of an exponential - type function

For an exponential function of the form $y = a^x$ (here $a = 3$) and $f(x)=3^x + 5$, $x$ can take any real - number value. So the domain of $y = 3^x+5$ is $(-\infty,\infty)$ because there are no restrictions on the input $x$ for the exponential function $3^x$.

Step2: Determine the range of the exponential function $y = 3^x$

The exponential function $y = 3^x$ has a range of $(0,\infty)$ since for any real number $x$, $3^x>0$.

Step3: Determine the range of $y = 3^x + 5$

If $y = 3^x+5$ and $3^x>0$, then adding 5 to both sides of the inequality gives $3^x + 5>5$. So the range of $y = 3^x+5$ is $(5,\infty)$.

Answer:

domain: $(-\infty,\infty)$; range: $(5,\infty)$