# How to Graph Exponential Functions?

An exponential function is a Mathematical function in form $$f(x)=a^x$$. We can plot diagrams of the exponential function. Learn how to plot exponential function by the following step-by-step guide.

In mathematics, an exponential function is a function of form $$f(x)=a^x$$, Where $$x$$ is a variable and $$a$$ is a constant called the base of the function and must be greater than $$0$$.

## Step by step guide to exponential function graph

We can understand the process of graphing exponential function with examples. Let us graph two functions $$f(x)=2^x$$ and $$g(x)=(\frac{1}{2})^2$$.

To plot each of these functions, we create a table of values with random values $$x$$, plot the points on the chart, connect them by a curve, and extend the curve on both sides.

Here is the table of values that are used to graph the exponential function $$f(x)=2^x$$.

Here is the table of values that are used to graph the exponential function $$g(x)=(\frac{1}{2})^2$$.

Note: the graph of exponential function $$f(x)=b^x$$:

• increases when $$b > 1$$
• decreases when $$0 < b < 1$$

### Domain and Range of Exponential Function

The domain of a function $$y = f (x)$$ is the set of all values of $$x$$ (inputs) that can be calculated, and the range is the set of all $$y$$-values (outputs) of the function. The domain of an exponential function is the set of all real numbers (or) $$(-∞, ∞)$$. The range of an exponential function can be determined by the horizontal asymptote of the graph, for example, $$y = d$$, and by seeing whether the graph is above $$y = d$$ or below $$y = d$$.

Therfore, for an exponential function $$f(x) = ab^x$$,

• Domain is the set of all real numbers (or) $$(-∞, ∞)$$.
• Range is $$f(x) > d$$ if $$a > 0$$ and $$f(x) < d$$ if $$a < 0$$.

## Exercises for Exponential Function Graph

### Plot the following exponential functions.

• $$\color{blue}{y=2^x+1}$$
• $$\color{blue}{y=4^{-x}}$$
• $$\color{blue}{y=2^x+1}$$
• $$\color{blue}{y=4^{-x}}$$

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