Consider the functions f(x)=ax^3 and g(x)=bx^3, where a and b are non-zero real constants. Find a size change that maps f(x) onto g(x)

Answer 1

f(x) = ax³

g(x) = bx³

f(x) will be the same as (that is, map onto) g(x) if we change the a to a b. ·So if we multiply f(x) by b/a:

(b/a)f(x) = (b/a)ax³ = bx³

b/a is a vertical dilation that stretches or compresses the graph of f(x) until it matches the graph of g(x).