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Unit 1 · 12 lessons

Characteristics of Functions

How to recognize, evaluate, transform and invert functions, and the algebra (quadratics, radicals, rational expressions) that supports working with them.

  • 132 practice questions
  • 110 flashcards
  • 1 interactive lesson
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Lessons

  1. 1Relations vs. FunctionsA function is a special kind of relation where every input produces exactly one output — learn to spot the difference and use function notation.12 questions
  2. 2Domain and RangeDomain is the complete set of valid inputs and range is the complete set of outputs a function can produce — find both from graphs, tables and equations.11 questions
  3. 3Parent FunctionsFive basic functions — linear, quadratic, square root, reciprocal, and absolute value — are the building blocks every transformed function is based on.11 questions
  4. 4Transformations of FunctionsThe single rule describes every stretch, compression, reflection and translation applied to a parent function.Interactive11 questions
  5. 5Inverse FunctionsThe inverse of a function reverses inputs and outputs; it's found algebraically by swapping x and y, and graphically it's a reflection in the line .11 questions
  6. 6Forms of a Quadratic RelationStandard, factored and vertex form all describe the same parabola, but each one reveals a different feature instantly — learn to read and convert between them.11 questions
  7. 7Completing the SquareCompleting the square rewrites any standard-form quadratic into vertex form algebraically, revealing the exact vertex and the maximum or minimum value.10 questions
  8. 8Solving Quadratic EquationsFactoring, the quadratic formula, and the discriminant give you three complementary tools for finding — or counting — the roots of a quadratic equation.11 questions
  9. 9Quadratic ApplicationsProjectile motion, area, and revenue problems all reduce to building a quadratic model and finding its vertex — the maximum or minimum of the situation.11 questions
  10. 10RadicalsSimplifying, combining, and rationalizing radicals — including using conjugates to clear a radical from a denominator.11 questions
  11. 11Rational ExpressionsAlgebraic fractions simplify, multiply, divide, add and subtract using the same rules as numeric fractions — but every step needs a restriction on the variable.11 questions
  12. 12Equivalent Algebraic ExpressionsTwo expressions are equivalent when they simplify to exactly the same expanded form — expand and simplify both sides to prove it.11 questions