An interesting function in mathematics
The exponential function is a concept that sounds extremely difficult to get your head around. What exactly is an exponential function? Fortunately, the explanation of this concept is much easier than you would imagine. The exponential function has the very simple formula: f(x) = a^x, with the ‘a’ having to be greater than zero in order to satisfy the condition that a > 0.
The name – intriguing and perhaps a little daunting to a rookie student of maths – comes from the fact that ‘x’ is in the exponent.
It is interesting to note that the graph of our function is such a curve that, no matter what, it always crosses the y-axis at point 1. However, depending on whether ‘a’ is greater than 1 or less than 1, it can look inverted.
The domain of any exponential function is the set of real numbers R – and its set of values are all positive and real numbers.
The graph that we get from an exponential function is called an exponential curve.
The exponential function has a number of domains or properties. Firstly, its domain is the set of real numbers. Secondly, only positive numbers belong to the set of values. Thirdly, the function can be either decreasing or increasing. In general, a function is differentiable. The value for the zero argument is 1. The graph IS NOT a straight line.
Contrary to popular belief, mathematics is not a difficult subject and can be learned. It is best when you practise because, as they say, practice makes perfect. It is worth looking for interesting tasks with solutions on the internet to practise your ability to calculate the exponential function. After a few such examples, you will find that you have mastered the material perfectly – and it is one of those things that can come in handy for your studies if you ever considering following the same career path as that of your teacher.
If you're still having trouble understanding what an exponential function is, it's worth reading this text a few times – the examples of graphs will help you better understand the issue and solve any tasks.
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