Final answer:
The rule for the transformed function g, which is a vertical shrink by a factor of 1/3 followed by a 5 units translation to the left of f(x) = √x, is g(x) = (1/3)√(x + 5).
Step-by-step explanation:
To write a rule for g, the given transformation of the function f(x) = √x, we need to apply a vertical shrink by a factor of 1/3, followed by a horizontal translation 5 units to the left.
Firstly, a vertical shrink by a factor of 1/3 to the function f(x) is achieved by multiplying the function by 1/3. This gives us a new function:
g(x) = (1/3)√x.
Secondly, to translate this function 5 units to the left, we replace x with x + 5:
g(x) = (1/3)√(x + 5).
Therefore, the rule for g that represents a vertical shrink by a factor of 1/3 followed by a translation of 5 units to the left of the graph of f(x) = √x is:
g(x) = (1/3)√(x + 5).
Complete Question:
Let the graph of g be a vertical shrink by a factor of 1/3 followed by a translation 5 units to the left of the graph of f(x)=√x. Write a rule for g.