In the previous post, we have learned how to analyze equations of functions and determine their domain and range. We have observed that the range of the functions and are the set of real numbers greater than or equal to since squaring a number or getting its absolute value results to or a positive real number. We also learned that for a function to be defined, the number under the square root sign must be greater than or equal to 0. Lastly, we have learned that we cannot divide by zero because it will make the function undefined.
In this post, we are going to continue our discussion by examining functions with equations more complicated than those in the second part of this series.
Squares and Absolute Values
Domain: The function is defined for any real number , so the domain of is the set of real numbers.
Range: The minimum value of is for any real number and . So, the minimum value of the function is . We can make the value of the function as large as possible by increasing the absolute value of . So, the range of the function is the set of real numbers greater than or equal to or in interval notation. » Read more