If it is possible to express the output as a formula involving the input quantity, then we can define a function. Notice that while the graph in the previous example is a function, getting two input values for the output value of 4 shows us that this function is not one-to-one. A function is rule for a relationship between an input, or independent, quantity and an output, or dependent, quantity in which each input value uniquely determines one output value. The natural world is full of relationships between quantities that change. When we see these relationships, it is natural for us to ask If I know one quantity, can I then determine the other? This establishes the idea of an input quantity, or independent variable, and a corresponding output quantity, or dependent variable.
Most often in business calculus, you do not work with trigonometric functions like sin or cos. In a regular calculus course however, you work with these in every topic – from limits to integrals. InputOutput215386InputOutput InputOutput105254The first and second tables define functions. The third table does not define a function since the input value of 5 corresponds with two different output values.
These may be touched upon in business calculus, but not on the same level – that time is spent on applications instead. There are some basic functions that it is helpful to know the name and shape of. For these definitions we will use \(x\) as the input variable and \(f\) as the output variable.
Apply appropriate differentiation techniques to obtain derivatives of various functions, including logarithmic and exponential functions. Business Calculus by Dale Hoffman, Shana Calloway, and David Lippman is a derivative work based on Dale Hoffman’s Contemporary Calculus. The course covers one semester of Business Calculus for college students and assumes students have had College Algebra.
It is strongly encouraged that you consult with your institution of choice to determine how these credits will be applied to their degree requirements prior to transferring your credit. Finding limits using a graph – a preview of one of the big ideas you will be working with. When solving an equation using formulas, you can check your answer by using your solution in the original equation to see if your calculated answer is correct. Not every relationship can be expressed as a function with a formula.