Calculus in business mathematics12/15/2023 With this information we would say a reasonable domain is feet. We could make an educated guess at a maximum reasonable value, or look up that the maximum circumference measured is about 119 feet. For the domain, possible values for the input circumference c, it doesn’t make sense to have negative values, so \(c > 0\). We could combine the data provided with our own experiences and reason to approximate the domain and range of the function \( h = f(c)\). Using the tree table above, determine a reasonable domain and range. For these definitions we will use \(x\) as the input variable and \(f(x)\) as the output variable. We call these the basic toolkit of functions. There are some basic functions that it is helpful to know the name and shape of. (input) \(a\), age in yearsĪ) To evaluate \(k(2)\), we plug in the input value 2 into the formula wherever we see the input variable \(t\), then simplify: While some tables show all the information we know about a function, this particular table represents just some of the data available for height and ages of children. This table represents the age of children in years and their corresponding heights. Represented as a table, we are presented with a list of input and output values. Tables as Functionsįunctions can be represented in many ways: Words (as we did in the last few examples), tables of values, graphs, or formulas. So this tells us that in the year 2005 there were 300 police officers in the town. The output value is 300, the number of police officers (\(N\)), a value for the output quantity. When we read \(f(2005) = 300\), we see the input quantity is 2005, which is a value for the input quantity of the function, the year (\(y\)). Be careful – the parentheses indicate that age is input into the function (Note: do not confuse these parentheses with multiplication!).Ī function \(N = f(y)\) gives the number of police officers, \(N\), in a town in year \(y\). The value \(a\) must be put into the function \(h\) to get a result. Remember we can use any variable to name the function the notation \(h(a)\) shows us that \(h\) depends on \(a\). We could instead name the function \(h\) and write Rather than write height is a function of age, we could use the descriptive variable \(h\) to represent height and we could use the descriptive variable \(a\) to represent age. We also use descriptive variables to help us remember the meaning of the quantities in the problem. To simplify writing out expressions and equations involving functions, a simplified notation is often used. To view this video please enable JavaScript, and consider upgrading to a web browser that supports HTML5 video Function Notation §2: Calculus of Functions of Two Variables.§2: The Fundamental Theorem and Antidifferentiation.§11: Implicit Differentiation and Related Rates.§6: The Second Derivative and Concavity.Here are the instructions how to enable JavaScript in your web browser. For full functionality of this site it is necessary to enable JavaScript.
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