Lesson Plan

Prove algebraically that for f(x) = mx + b, the difference f(x + d) - f(x) = md for any equal spacing d, showing the result is independent of x

Prove algebraically that for g(x) = a * b^x, the ratio g(x + d) / g(x) = b^d for any equal spacing d, showing the result is independent of x

Explain why the constant difference property is equivalent to a constant rate of change (slope)

Explain why the constant ratio property is equivalent to a constant growth/decay factor (base)

Use the proofs to determine whether a given function is linear or exponential without relying solely on tables of values

Connect the algebraic proofs to numerical examples by verifying the formulas with specific values of x and d

HSF.LE.A.1.a

HSF.LE.A.1.a: Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.