Question

let the graph of g be a translation 1 unit down and 3 units left of the graph of f(x)= |x-4| + 2. write a rule for g

Answer 1

Given the translation statement, the rule for the function g is g(x) = |x - 1| + 1

How to determine the rule for the function g

From the question, we have the following parameters that can be used in our computation:

f(x) = |x - 4| + 2

Also, we have

The function g is a translation

• 1 unit down
• 3 units left

This means that

g(x) = f(x + 3) - 1

Substitute the known values into the equation

g(x) = |x - 4 + 3| + 2 - 1

Evaluate

g(x) = |x - 1| + 1

Hence, the rule for the function g is g(x) = |x - 1| + 1