Question

Let g(x) be the transformation of f(x)= x2. Write the rule for g(x) using the change described.

1. horizontal shift 6 units to the left, vertical shift down by 5 followed by a compression horizontally by a factor of 1/3. ______________

Answer 1

$f(x)=x^2\\y=x^2$

now according to given condition

$y-5=\frac{1}{3}\times(x-6)^2\\y-5=\frac{1}{3}\times(x^2+36-12x)\\y-5=\frac{x^2}{3}+12-4x$

$y=\frac{x^2}{3}+17-4x\\f(x)=\frac{x^2}{3}+17-4x$