Question

What is the effect on the graph of the function f(x) = 2x when f(x) is replaced with f( 2/3

x)? A)vertical stretching B)vertical compression C)horizontal compression D) horizontal stretching

Answer 1

`\bf f(x)=2x\qquad \qquad f\left( (2)/(3)x \right)=2\left( (2)/(3)x \right)\implies f\left( (2)/(3)x \right)=\cfrac{4}{3}x \\\\\\ now\quad \cfrac{4}{3}\iff 1\cfrac{1}{3}\textit{ that's smaller than }2`

f(x) = A(Bx+C)+D

any changes to A or B are vertical compressions
if you change the A from 2 to 4/3, the number is smaller than before

the smaller the A, the wider the graph, the larger the A, the more compressed the graph