Add, subtract, multiply, and divide functions

Learning Objectives Define and notate the sum, difference, product, and quotient of functions. Compute the algebraic expressions for (f+g)(x), (f-g)(x), (f*g)(x), and (f/g)(x) given f(x) and g(x). Evaluate combinations of functions at a specific numerical value, such as (f+g)(2). Determine the domain of a new function created by adding, subtracting, or multiplying two functions by finding the intersection of their original domains. Determine the domain of a quotient of two functions, ensuring the denominator is not equal to zero. Apply the concept of function operations to model and solve contextual problems. Ever wondered how a company combines its revenue and cost functions to find its profit function? 📈 It's just a simple subtraction of functions! Just like numbers...

TermDefinitionExample Sum of FunctionsThe new function created by adding the outputs of two functions, f(x) and g(x), for every x-value in their common domain.If f(x) = x^2 and g(x) = 2x, then the sum function is (f+g)(x) = x^2 + 2x. Difference of FunctionsThe new function created by subtracting the outputs of two functions, f(x) and g(x), for every x-value in their common domain.If f(x) = 3x + 5 and g(x) = x + 1, then the difference function is (f-g)(x) = (3x + 5) - (x + 1) = 2x + 4. Product of FunctionsThe new function created by multiplying the outputs of two functions, f(x) and g(x), for every x-value in their common domain.If f(x) = x and g(x) = x - 7, then the product function is (f*g)(x) = x(x - 7) = x^2 - 7x. Quotient of FunctionsThe new function created by dividing the outputs of...

Sum Rule (f+g)(x) = f(x) + g(x) To find the sum of two functions, add their expressions. The domain of (f+g) is the intersection of the domains of f and g, written as D_f ∩ D_g. Difference Rule (f-g)(x) = f(x) - g(x) To find the difference, subtract the second function's expression from the first. The domain of (f-g) is the intersection of the domains of f and g, D_f ∩ D_g. Product Rule (f \cdot g)(x) = f(x) \cdot g(x) To find the product, multiply their expressions. The domain of (f*g) is the intersection of the domains of f and g, D_f ∩ D_g. Quotient Rule \left(\frac{f}{g}\right)(x) = \frac{f(x)}{g(x)} To find the quotient, divide the first function's expression by the second. The domain is the intersection of the domains of f and g, excluding any...