Question

The function f(x)= square root of x is translated using the rule (x, y) → (x – 6, y + 9) to create A(x). Which expression describes the range of A(x)?

Answer 1

The function $f(x)=\sqrt{x}$ is translated according to the rule

$(x,y)\rightarrow (x-6,y+9).$

This translation is translation 6 units to the left and 9 units up.

1. Translation of the function $f(x)=\sqrt{x}$ 6 units to the left gives you the function $g(x)=\sqrt{x+6}.$

2. Translation of the function $g(x)=\sqrt{x+6}$ 9 units up gives you the function $A(x)=\sqrt{x+6}+9.$

The domain of the function $A(x)$ is $[-6,\infty),$ then the range of the function $A(x)$ is $[9,\infty).$

Answer: $[9,\infty).$