I know the Geometric proof just by plotting the points and looking at the graphs. But I need to know the algebraic proof of (vertical stretching and shrinking graph rule) . What is the proof?

Question

Don't restate the rules or give examples. I just need the proof for all type of function. Thank you.

Answer 1

y₁ = f(x)

y₂ = a(f(x))

y₂ = ay₁