1. The problem is to find the domain and range for the function $y=4^x$. 2. The domain of an exponential function $y=a^x$ where $a>0$ and $a \neq 1$ is all real numbers because $x$ can be any real number. So domain is $$(-\infty, \infty)$$. 3. The range of $y=4^x$ is all positive real numbers because $4^x>0$ for any real $x$ and as $x\to -\infty$, $4^x \to 0$ but never equals zero. As $x\to \infty$, $4^x \to \infty$. So range is $$(0, \infty)$$. 4. Final answer: Domain is $$(-\infty, \infty)$$ and Range is $$(0, \infty)$$.