What can you do with an exponential function?
It is mainly used to find the exponential decay or exponential growth or to compute investments, model populations and so on. In this article, you will learn about exponential function formulas, rules, properties, graphs, derivatives, exponential series and examples.
Which is the domain of an exponential function?
The domain of exponential function will be the set of entire real numbers R and the range are said to be the set of all the positive real numbers. It must be noted that exponential function is increasing and the point (0, 1) always lies on the graph of an exponential function.
How is the derivative of an exponential function expressible?
The derivative (rate of change) of the exponential function is the exponential function itself. More generally, a function with a rate of change proportional to the function itself (rather than equal to it) is expressible in terms of the exponential function. This function property leads to exponential growth or exponential decay.
Which is the probability density function of an exponential distribution?
The probability density function (pdf) of an exponential distribution is. Alternatively, this can be defined using the right-continuous Heaviside step function, H(x) where H(0) = 1: Here λ > 0 is the parameter of the distribution, often called the rate parameter. The distribution is supported on the interval [0, ∞).
How can I graph an exponential function using transformations?
Graphing Exponential Functions Using Transformations Transformations of exponential graphs behave similarly to those of other functions. Just as with other parent functions, we can apply the four types of transformations—shifts, reflections, stretches, and compressions—to the parent function f(x) = bx without loss of shape.
Which is a property of the exponential graph?
The exponential graph of a function represents the exponential function properties. The graph of function y=2 x is shown below. First, the property of the exponential function graph when the base is greater than 1. The graph passes through the point (0,1). The graph of function y=2 -x is shown above.