What you’ll learn
Understand f(x)+k.
Key idea
Outside addition changes every output by the same amount and keeps each input.
Outside addition preserves input and adds the same signed amount to each output.
Worked example
Classify examples and non-examples for the concept 'Understand f(x)+k'.
For g(x)=f(x)-5, classify the transformation and map point (-2,1) on f.
- The addition is outside f, so input remains -2 and output 1 gains signed -5.
- Point (-2,1) maps to (-2,-4), and (-1,3) to (-1,-2); vertical shift down 5.
Answer: Vertical shift down 5 — (-2,1) becomes (-2,-4).
Quick Check
Classify examples and non-examples for the concept 'Understand f(x)+k'.
For g(x)=f(x)-5, classify the transformation and map point (1,-5) on f.