which best describes the range of the function (f(x)=2(3)^{x})?\n(y > 0)\n(ygeq0)\n(y > 2)\n(ygeq2)
which best describes the range of the function (f(x)=2(3)^{x})?\n(y > 0)\n(ygeq0)\n(y > 2)\n(ygeq2)
Answer
Explanation:
Step1: Analyze the exponential function
The general form of an exponential function is $y = a\cdot b^x$, where $a = 2$ and $b=3$ in $f(x)=2(3)^x$. The exponential part $b^x = 3^x$, and for any real - number $x$, $3^x>0$ since the base $b = 3>1$ and the exponential function $y = b^x$ with $b>0,b\neq1$ has a range of $(0,+\infty)$ for all real $x$.
Step2: Consider the coefficient
We have $y = 2(3)^x$. Since $3^x>0$ for all real $x$, when we multiply $3^x$ by 2, we get $y=2(3)^x>0$.
Answer:
A. $y > 0$