Question

let the graph of g be horizontal shrink by the factor of 2/3 followed by a translation 5 units left and 2 units down of the graph of f (x) =x ^ 2​

Answer 1

1. horizontal shrink by factor of 2/3 means multiply outside the f(x) or outside the x^2 by 2/3:

   (2/3)•f(x)

2. translation left 5 units means "x+5" inside:

   (2/3) • f(x+5)

3. tranlate down 2 units means "-2" outside:

      (2/3) • f(x+5) -2

or    (2/3) (x+5)^2 - 2

$\frac{2}{3}\cdot f(x+5)-2$   or   $\frac{2}{3}\cdot (x+5)^2-2$