Introduction to domain and range of exponential functions:
A function gives the output values for various values assigned to the variable. That means for every value of the variable there is a corresponding value of the function. However, in certain functions, for some values of the variable, the function may not be defined. The study of such values of the variable and the corresponding values of the function is called the study of domain and range of the function.
In this section we will study the domain and range of exponential functions.
Domain and Range of Exponential Functions – Description
It is important to identify the set of the variables that only make the function exist. This set of values is defined as the domain of the function. Similarly the values of the function undergoes limitations. It is possible that the variable can be assigned any real number but the function values may be only within an interval. This interval of the values of the function is called the range of the function.
An exponential function means a function where the variable is in the place of exponent. In the simplest form it is defined by,
f(x) = akx , where a and k are constants.
This function needs to be studied because it does have certain limitations. I have recently faced lot of problem while learning Formula for Simple Interest, But thank to online resources of math which helped me to learn myself easily on net.
Domain and Range of Exponential Functions – Domain and Range
Consider an exponential function defined by,
f(x) = akx , where a and k are constants.
In the above function you are free to assign all real numbers for the variable.
Assuming k to be positive, the lesser and lesser values of the variable in the negative direction, the value of the function becomes smaller and smaller but remaining positive always. At the ultimate when x tends to minus infinity, the value of the function tends to 0.
Again assuming k to be positive, the grater and greater values of the variable in the positive direction, the value of the function becomes larger and larger but remaining positive always. At the ultimate when x tends to infinity, the value of the function also tends to infinity.
Therefore, the conclusion is the domain of an exponential function is all real numbers and the range is all positive real numbers.
A function gives the output values for various values assigned to the variable. That means for every value of the variable there is a corresponding value of the function. However, in certain functions, for some values of the variable, the function may not be defined. The study of such values of the variable and the corresponding values of the function is called the study of domain and range of the function.
In this section we will study the domain and range of exponential functions.
Domain and Range of Exponential Functions – Description
It is important to identify the set of the variables that only make the function exist. This set of values is defined as the domain of the function. Similarly the values of the function undergoes limitations. It is possible that the variable can be assigned any real number but the function values may be only within an interval. This interval of the values of the function is called the range of the function.
An exponential function means a function where the variable is in the place of exponent. In the simplest form it is defined by,
f(x) = akx , where a and k are constants.
This function needs to be studied because it does have certain limitations. I have recently faced lot of problem while learning Formula for Simple Interest, But thank to online resources of math which helped me to learn myself easily on net.
Domain and Range of Exponential Functions – Domain and Range
Consider an exponential function defined by,
f(x) = akx , where a and k are constants.
In the above function you are free to assign all real numbers for the variable.
Assuming k to be positive, the lesser and lesser values of the variable in the negative direction, the value of the function becomes smaller and smaller but remaining positive always. At the ultimate when x tends to minus infinity, the value of the function tends to 0.
Again assuming k to be positive, the grater and greater values of the variable in the positive direction, the value of the function becomes larger and larger but remaining positive always. At the ultimate when x tends to infinity, the value of the function also tends to infinity.
Therefore, the conclusion is the domain of an exponential function is all real numbers and the range is all positive real numbers.
