Domain Exponential Graph

Graphs of the complex exponential function.

Domain exponential graph. The domain of latex f left x right 2 x latex is all real numbers the range is latex left 0 infty right latex and the horizontal asymptote is latex y 0 latex. Also it is very close to zero if the value of x is mostly negative. The graph of f has a horizontal asymptote given by y 0.

The graph of this function crosses the y y axis at 0 1 0. Notice that the graph gets close to the x axis but never touches it. The corresponding point on the graph is shown as well as the value of f x.

In general the graph of the basic exponential function y a x drops from to 0 when 0 a 1 as x varies from to and rises from 0 to when a 1. The domain of f x 2 x is all real numbers the range is 0 infty and the horizontal asymptote is y 0. Improve your math knowledge with free questions in domain and range of exponential functions.

1 and increases as x x approaches infinity. The exponential function y a x can be shifted k units vertically and h units horizontally with the equation y a x h k. The graph below shows the exponential growth function latex f left x right 2 x latex.

We first start with the properties of the graph of the basic exponential function of base a f x a x a 0 and a not equal to 1. To get a sense of the behavior of exponential decay we can create a table of values for a function of the form f x b x whose base is between zero and one. Starting with a color coded portion of the domain the following are depictions of the graph as variously projected into two or three dimensions.

It must be noted that exponential function is increasing and the point 0 1 always lies on the graph of an exponential function. Graph of y 2x y 2 x. The graph of the exponential function is a two dimensional surface curving through four dimensions.