What you’ll learn
Understand af(x).
Key idea
Multiply each output by the signed factor; its magnitude and sign have different geometric roles.
Multiplication preserves inputs and changes output ratios; it is not a constant translation.
Worked example
Classify examples and non-examples for the concept 'Understand af(x)'.
Classify g(x)=(-3)f(x), including factor magnitude/sign, and map (1,2) on f.
- Outside multiplication by -3 keeps input 1, changes output 2 to -6.
- The next point (2,3) maps to (2,-9); output ratios are -3. Magnitude 3 gives vertical stretch with reflection across the x-axis.
Answer: Vertical stretch by 3 with reflection across the x-axis — (1,2) becomes (1,-6).
Quick Check
Classify examples and non-examples for the concept 'Understand af(x)'.
Classify g(x)=(-2)f(x), including factor magnitude/sign, and map (1,2) on f.