1. The problem is to find the function that fits the user's query and to provide a detailed explanation with steps. 2. Here we assume the function is $y=a^x$ with $a>0$ and $a\ne 1$ as per plotting instruction. 3. The function $y=a^x$ is an exponential function where the base $a$ determines the growth (if $a>1$) or decay (if $00$ for all $x$. 6. The function is strictly increasing if $a>1$ and strictly decreasing if $0