Graph the function and write the domain and range in interval notation.
\[
f(x)=2^{x}
\]
Part: $0 / 2$
Part 1 of 2
Graph the function $f(x)=2^{x}$.
\(\boxed{\text{The domain of } f(x)=2^{x} \text{ is } (-\infty, \infty) \text{ and the range is } (0, \infty)}\)
Step 1 :The function \(f(x)=2^{x}\) is an exponential function with base 2.
Step 2 :The graph of an exponential function is always above the x-axis (y>0) and it increases as x increases.
Step 3 :The y-intercept is at (0,1) because any number to the power of 0 is 1.
Step 4 :The graph of the function \(f(x)=2^{x}\) is a curve that starts from the y-axis at point (0,1) and increases as x increases.
Step 5 :The domain of the function is all real numbers, and the range of the function is all positive real numbers.
Step 6 :In interval notation, the domain is \((-\infty, \infty)\) and the range is \((0, \infty)\).
Step 7 :\(\boxed{\text{The domain of } f(x)=2^{x} \text{ is } (-\infty, \infty) \text{ and the range is } (0, \infty)}\)