![]() ![]() A student armed with this basic knowledge will be more confident in her or his work, and is better equipped to solve the problems we will encounter. While the calculator is a powerful tool for us to use in calculus, there is no substitute for basic knowledge of the things we study, independent of the calculator. No doubt you have access to a graphing calculator so you may wonder why worry so much about the graph when you can just plug the function into your calculator and get its graph. Graph: The graph is the set of points \((a,b)\) such that \(f(a)=b\text\) Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x x -axis. ![]() Range: The range is the set of values the function assumes. While complex numbers have many important properties, our focus here is on real numbers only.ģ: Context - There are other restrictions that depend upon the nature of specific functions (some of which we will encounter soon) and also from the context of the problem we wish to solve. There are generally three restrictions we need to consider to help us determine the range of a function:ġ: Division by zero - It is impossible to divide by zero so we will need to eliminate from the domain all values that lead to division by zero.Ģ: Negatives under square roots (or any even root) - The square root of a negative number is a complex number, not a real number. We make up the domain of a graph with all the x-axis input data. However, we call the set of possible inputs, the domain. We can also use graphs to determine the domain and range of functions. Domain: The domain is the set of values for which the function is defined. All trigonometric functions have the following domain and range: Domain and Range Calculator Graph. ![]()
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