MEI

Mappings Lab

Mathematics for Engineers I · Module 62765 · Chapter 3

Predict what the mapping, graph, or point will do. Rate your confidence, reveal the mechanism, then explore new values after the four challenges.

How the lab works

  1. Predict. Commit to an answer before the stage changes.
  2. Rate your confidence. A sure but wrong answer marks an idea to revisit first.
  3. Reveal. Follow the inputs through the rule and compare the result with your prediction.
  4. Explore. Finish all four challenges to unlock that experiment’s controls.

3.1–3.2 Mapping types: where each input lands

Follow a finite set through a rule. Collisions reveal non-injectivity; codomain values with no incoming arrow reveal non-surjectivity.

After the challenges, choose a rule below, or type your own rule and sets.

Choose the mapping
Or try your own

Use x, + − × ÷ ^, brackets, sqrt, abs, sin, cos, tan, exp, ln, pi.

3.3 Inverse functions: restrict, then reverse

A horizontal line meeting a graph twice signals that reversing the rule would give one output two possible inputs. Restricting the original domain can restore a unique inverse.

After the challenges, choose a function below, or type your own and drag the horizontal line on the stage.

Inspect the function
Or try your own

Use x, + − × ÷ ^, brackets, sqrt, abs, sin, cos, tan, exp, ln, pi.

3.4 Composition: order and domain

Track an input through the first rule and then the second. The chain stops wherever an intermediate value falls outside the next function’s domain.

After the challenges, choose a composition below, or type your own two rules.

Choose a composition
Or try your own

Use x, + − × ÷ ^, brackets, sqrt, abs, sin, cos, tan, exp, ln, pi.

3.5 Elementary functions: graph and domain

Different rules bring different restrictions. Inspect the curve and decide where a value exists, repeats, or vanishes.

After the challenges, choose a family below, or type your own rule.

Choose a function family
Or try your own

Use x, + − × ÷ ^, brackets, sqrt, abs, sin, cos, tan, exp, ln, pi.

3.6 Polar coordinates: radius and angle

Rotate a radius from the positive x-axis, then read its horizontal and vertical components. The same point can have many angle descriptions.

After the challenges, drag the point on the stage, or choose the angle and the radius below.

Choose the angle

Your results

Scores are saved in this browser. “Sure, but wrong” highlights confident mistakes to revisit in the guide.

Personal interactive lab based on Mathematics for Engineers I lecture notes, Chapter 3 “Mappings” (printed pages 23–35), by Rhoslyn Coles and Cornelia Schneider. Not an official FAU publication; check course details against the current notes. Made by Thanate Amornjiraporn (Focus).