Write an equation for f(x)=|x| after being translated to the right 3 units and down 8 unites.
Part A: What is being asking in the problem and what that mean? What plan am I going to try?
Part B: Solve
Part A: The problem is asking for an equation for the function f(x) = |x| after it has been translated to the right 3 units and down 8 units. This means that the original function |x| will be shifted horizontally by 3 units to the right and vertically by 8 units downwards. To find the equation, we need to determine how to represent these translations mathematically.
Part B: To solve the problem, we can use the general form of the equation for a translation: f(x) = |a(x - h)| + k, where (h, k) represents the horizontal and vertical shifts, respectively.
In this case, the function f(x) = |x| has been translated 3 units to the right and 8 units down. Thus, the value of h (horizontal shift) is 3, and the value of k (vertical shift) is -8.
Plugging these values into the general equation, we have f(x) = |(x - 3)| + (-8). Simplifying further, we get f(x) = |x - 3| - 8.
So, the equation for f(x) = |x| after being translated to the right 3 units and down 8 units is f(x) = |x - 3| - 8.