Worked Example: Diagnostic Problem Solutions

Calculus Readiness · Axiom Academy

Factor the quadratic x^2 + 7x + 12 into a product of two binomials. Given f(x) = -2x + 5 , evaluate f(-3) . Find the inverse of f(x) = 3x - 2 . Four readiness skills, one move each — once you can name the move, the problem unlocks. Factoring: find two numbers that multiply to the constant and add to the middle coefficient, then always confirm by expanding. Function notation: means substitute that input for x ; mind the signs — a negative times a negative is positive. Exponent rules: multiplying same-base powers adds the exponents: . Inverses: swap x and y , then solve for y ; the inverse is what undoes the function, not its reciprocal. Recognizing which move a problem is asking for is the readiness skill itself — the algebra after that is mechanical.

This is the written version of the interactive lesson above. See the full Calculus Readiness course.