Domain and range of log

Domain and Range of Exponential and Logarithmic Functions

domain and range of log

A simple exponential function like f(x)=2x f (x) = 2 x has as its domain the whole real line. But its range is only the positive real numbers, y>0:f(x) y > 0: f (x) never takes a negative value. The inverse of an exponential function is a logarithmic function.

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Logarithmic functions are the inverses of exponential functions. It is called the logarithmic function with base a. Given a number x and a base a , to what power y must a be raised to equal x? This unknown exponent, y , equals log a x. So you see a logarithm is nothing more than an exponent. Notice that the domain consists only of the positive real numbers, and that the function always increases as x increases. The domain of a logarithmic function is real numbers greater than zero, and the range is real numbers.

Wolfram Alpha is a great tool for finding the domain and range of a function. It also shows plots of the function and illustrates the domain and range on a number line to enhance your mathematical intuition. Enter your queries using plain English. To avoid ambiguous queries, make sure to use parentheses where necessary. Here are some examples illustrating how to ask for the domain and range. For example, a function that is defined for real values in has domain , and is sometimes said to be "a function over the reals. Informally, if a function is defined on some set, then we call that set the domain.

The function is defined for all real numbers. So, the domain of the function is set of real numbers. Remember that since the logarithmic function is the inverse of the exponential function, the domain of logarithmic function is the range of exponential function, and vice versa. Note that the logarithmic functionis not defined for negative numbers or for zero. However, the range remains the same. Graph the function on a coordinate plane.

Before working with graphs, we will take a look at the domain the set of input values for which the logarithmic function is defined. So, as inverse functions:. Just as with other parent functions, we can apply the four types of transformations—shifts, stretches, compressions, and reflections—to the parent function without loss of shape. Therefore, when finding the domain of a logarithmic function, it is important to remember that the domain consists only of positive real numbers. That is, the value you are applying the logarithmic function to, also known as the argument of the logarithmic function, must be greater than zero. Solving this inequality,. Now that we have a feel for the set of values for which a logarithmic function is defined, we move on to graphing logarithmic functions.

Therefore it is one-to-one and has an inverse. Recall that if x , y is a point on the graph of a function, then y , x will be a point on the graph of its inverse. To find the inverse algebraically, begin by interchanging x and y and then try to solve for y. We quickly realize that there is no method for solving for y. The following are equivalent:.

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Domain and Range of Exponential and Logarithmic Functions




Domain of Logarithmic Functions





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