What you’ll learn
Understand f(x−h).
Key idea
Solve the inside argument equal to the original input to locate its new position.
Solve the inner argument equal to old input; point displacement is opposite the written inner constant.
Worked example
Classify examples and non-examples for the concept 'Understand f(x−h)'.
Classify g(x)=f(x+5) and map (0,2) from f.
- For the original input 0, solve new_input--5=0, giving new_input=-5.
- Correspondence (0,2)→(-5,2) and (1,4)→(-4,4) preserves heights; shift left 5.
Answer: Horizontal shift left 5 — (0,2) becomes (-5,2).
Quick Check
Classify examples and non-examples for the concept 'Understand f(x−h)'.
Classify g(x)=f(x+4) and map (-2,2) from f.