Problem

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 $f(x)=2^{x}$.

Solution

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 :\(\boxed{\text{The domain of } f(x)=2^{x} \text{ is } (-\infty, \infty) \text{ and the range is } (0, \infty)}\)

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Source: https://solvelyapp.com/problems/q8B8qVQRl0/

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