Lesson Plan

State the pointwise definition $(f+g)(x) = f(x) + g(x)$, and the corresponding definitions for difference, product, and quotient

Evaluate $(f+g)(a)$, $(f-g)(a)$, $(fg)(a)$, and $(f/g)(a)$ from the two functions' values at $a$

Write the simplified expression for a sum, difference, or product of two polynomial functions, distributing a subtraction correctly

Identify the values excluded from a quotient function because the divisor function is zero there, and explain why neither original function shows the restriction

Build a combined function in an applied setting — profit as revenue minus cost — and interpret its parameters and its zero

A 505. Add, subtract, and multiply polynomials A 513. Determine when an expression is undefined AF 602. Build functions and write expressions, equations, and inequalities for common algebra settings (e.g., distance to a point on a curve and profit for variable cost and demand) AF 702. Build functions and write expressions, equations, and inequalities when the process requires planning and/or strategic manipulation AF 703. Analyze and draw conclusions based on properties of algebra and/or functions A 403. Solve routine first-degree equations