select all interval(s) where ( f(x) ) only increases. select all that apply.\n( (-infty,-1) )\n( (4,7) )\n(…

Explanation:

Step1: Analyze function's increasing trend

A function (y = f(x)) is increasing on an interval if, for any two points (x_1) and (x_2) in the interval with (x_1<x_2), we have (f(x_1)<f(x_2)). From the graph, we can observe the vertex (low - point) of the parabola (assuming it's a quadratic function). Let's assume the vertex (x) - coordinate is (x = - 1) (by visual inspection of the graph's symmetry).

Step2: Determine the increasing interval

For a parabola (y = ax^{2}+bx + c) ((a>0), since the parabola opens upwards), the function is decreasing on ((-\infty,x_{vertex})) and increasing on ((x_{vertex},\infty)). Here (x_{vertex}=-1), so the function is increasing on ((-1,\infty))

Answer:

((-1,\infty))