1. The problem is to analyze the function $y=2^x$. 2. This is an exponential function where the base is 2 and the exponent is the variable $x$. 3. The general form of an exponential function is $y=a^x$ where $a>0$ and $a \neq 1$. 4. Important properties: - The function passes through the point $(0,1)$ because $2^0=1$. - The function is always positive, so $y>0$ for all real $x$. - As $x \to \infty$, $y \to \infty$. - As $x \to -\infty$, $y \to 0$. 5. To find intercepts: - $y$-intercept: set $x=0$, $y=2^0=1$. - $x$-intercept: set $y=0$, but $2^x$ never equals 0, so no $x$-intercept. 6. To find extrema: - The derivative is $y' = 2^x \ln(2)$ which is always positive, so the function is strictly increasing and has no local maxima or minima. Final answer: The function $y=2^x$ has a $y$-intercept at $(0,1)$, no $x$-intercept, and no extrema. It is strictly increasing and always positive.