Question

identify the domain, range, intercept, and asymptote of the exponential function. then describe the end behavior.\\( f(x) = 7 cdot 3^x \\)\\( \\)\\( \\)find the domain of \\( f(x) = 7 cdot 3^x \\). choose the correct answer below and, if necessary, fill in the answer box to complete your choice.\\( \\)\\( \bigcirc \\) a. \\( \\{x|x = \square\\} \\)\\( \quad \\) (use a comma to separate answers as needed.)\\( \bigcirc \\) b. \\( \\{x|x < \square\\} \\)\\( \bigcirc \\) c. \\( \\{x|x > \square\\} \\)\\( \bigcirc \\) d. \\( \\{x|x \
eq \square\\} \\)\\( \quad \\) (use a comma to separate answers as needed.)\\( \bigcirc \\) e. all real numbers

Explanation:

Step1: Analyze exponential function domain

For any exponential function of the form $f(x) = a \cdot b^x$ where $a
eq 0$, $b>0$, $b
eq 1$, the input $x$ can be any real number, since you can raise a positive real base to any real exponent.

Step2: Match to given options

The function $f(x)=7 \cdot 3^x$ fits this form, so its domain is all real numbers, which corresponds to option E.

Answer:

E. All real numbers