Multiply functions

Learning Objectives Correctly use the notation for the product of two functions. Algebraically determine the new function created by multiplying two functions, such as polynomials or rational functions. Determine the domain of a product of two functions by finding the intersection of their individual domains. Evaluate the product of two functions at a specific input value. Distinguish between multiplying functions, (f * g)(x), and composing functions, f(g(x)). Simplify the resulting product function by combining like terms or factoring. Imagine a company's revenue is a function of time, and its profit margin is another. How could you create a new function to model their total profit over time? 📈 This tutorial will guide you through the process of multiplying functions...

TermDefinitionExample FunctionA relation between a set of inputs (the domain) and a set of possible outputs (the range) where each input is related to exactly one output.f(x) = 3x + 2 is a linear function. For an input of x=5, the unique output is f(5) = 3(5) + 2 = 17. Domain of a FunctionThe complete set of all possible input values (x-values) for which the function is defined.For the function g(x) = 1/(x-4), the domain is all real numbers except x=4, because at x=4, the denominator would be zero. We write this as {x | x ≠ 4}. Product of FunctionsA new function created by multiplying the output values of two or more existing functions for each input value in their common domain.If f(x) = x and g(x) = x + 1, their product is (f * g)(x) = f(x) * g(x) = x(x + 1) = x² + x. Polynomial Functio...

The Product Rule for Functions (f \cdot g)(x) = f(x) \cdot g(x) This is the fundamental definition for multiplying two functions, f(x) and g(x). The notation (f * g)(x) means to create a new function by multiplying the expressions for f(x) and g(x). The Domain of a Product Function Domain(f \cdot g) = Domain(f) \cap Domain(g) The domain of the product function (f * g) is the intersection of the domains of the individual functions f and g. An input 'x' must be valid for both f(x) and g(x) to be valid for their product.