identify the interval where the function is increasing. 3<x<6 -2<x<0 x>3 x>-2
identify the interval where the function is increasing. 3<x<6 -2<x<0 x>3 x>-2
Answer
Answer:
$x>3$
Explanation:
Step1: Understand the concept of increasing function
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)). Graphically, the function has a positive slope.
Step2: Analyze the graph
Looking at the parabola (quadratic function (y = ax^{2}+bx + c,a>0)), its vertex form is (y=a(x - h)^{2}+k). The axis of symmetry is (x = h). For a parabola (y = ax^{2}+bx + c) with (a>0), the function is decreasing on the interval ((-\infty,h)) and increasing on the interval ((h,\infty)). From the graph (by observing the direction of the curve), the vertex (minimum point) occurs at (x = 3). So, the function is increasing for (x>3).