Question

state whether the function is bounded above, bounded below, or bounded.
y = 2^x
a. bounded above
b. bounded below
c. bounded
please select the best answer from the choices provided.

Explanation:

Step1: Analyze the range of the function

For the exponential function $y = 2^{x}$, where $x\in(-\infty,\infty)$. As $x\to-\infty$, $\lim_{x\to-\infty}2^{x}=0$, but $2^{x}>0$ for all real - valued $x$. As $x\to\infty$, $\lim_{x\to\infty}2^{x}=\infty$.

Step2: Determine the boundedness

Since $y = 2^{x}>0$ for all $x\in R$, the function has a lower - bound of $0$ (but never reaches $0$), and there is no upper - bound as the function values increase without bound as $x$ increases. So the function is bounded below.

Answer:

B. bounded below