Question

Consider the graph of the function f(x) = 2(x + 3)2 + 2. Over which interval is the graph decreasing? (–∞, –3) (–∞, 2) (–3, ∞) (2, ∞)

Answer 1

A. (–∞, –3)

Explanation:

Answer 2

(–∞, –3)

Explanation:

The function
`f(x) = 2(x + 3) ^ 2 +2` is a quadratic function of order 2 and positive coefficient.

This is in the form of the function
`y = x^2`, but it is displaced 3 units to the left of the x axis and two units up in the y axis. type of functions are decreasing from -∞ to its vertex and then they are increasing from the vertex to infinity.

Observe in the attached graph that this function has its vertex in the point (-3, 2) and is decreasing from -∞ to x = -3. Then it is increasing until ∞. Therefore the correct option is:

(-∞, -3)