Question

HELP PLEASE?! Determine a radical function that starts at the point (-4,2) and goes to the right and decreases. The domain is all x>-4 and the range is all y<2. Explain how you determined you function.

Answer 1

Answer:

f(x) = -√(x-4) + 2

Step-by-step explanation:

(a) Start with the basic function: f(x) = √x.

This would be the top half of a horizontal parabola opening to the right (always positive).

(b) The range is y < 2. This includes negative numbers, so the function must be f(x) = -√x.

(c) The function starts at x = -4. We must shift it four units to the left. We do that by adding four units to x. The function must be f(x) = -√(x + 4). The domain is x > -4.  

(d) The function starts at y = 2. We must shift it up two units. We do that by adding two units to y. The function must be f(x) = -√(x+4) + 2. The range is y < 2.

The figure below is the graph of f(x) = -√(x+4) + 2.