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# Exponential Functions

## Definition of an Exponential Function

Previously, you have studied functions that have terms where the base is a variable and the exponent is a constant. For example,

In this lesson, you will study exponential functions. Exponential functions have terms where the base is a constant and the exponent contains a variable.

Definition â€” Exponential Function

An exponential function is a function that has the form:

f(x) = bx

where b and x are real numbers, b > 0, and b 1.

The domain is all real numbers.

The range is all positive real numbers.

Note:

We restrict the values of the base, b, so that the function f(x) = bx is a one to one function. 1.

A multiple of an exponential function is also an exponential function. This includes the following forms:
 General form  f(x) = A Â· bx  f(x) = C + A Â· bx Examplef(x) = 5 Â· 2x f(x) = -3 + 7 Â· 5x

Note the similarities and differences between the graphs of linear, quadratic, and exponential functions:

 Linear: f(x) = 2x (straight line) Quadratic: f(x) = x2 (parabola) Exponential: f(x) = 2x (a curve)