over what interval is the function increasing, and over what interval is the function decreasing?\n| x |…

over what interval is the function increasing, and over what interval is the function decreasing?\n| x | f(x)= - 0.1x² | (x,y) |\n| - 2 | - 0.4 | (-2, - 0.4) |\n| - 1 | - 0.1 | (-1, - 0.1) |\n| 0 | 0 | (0,0) |\n| 1 | - 0.1 | (1, - 0.1) |\n| 2 | - 0.4 | (2, - 0.4) |\nthe function f(x) is increasing over the interval x < 0\n(simplify your answer. type an inequality.)\nthe function f(x) is decreasing over the interval \n(simplify your answer. type an inequality.)

over what interval is the function increasing, and over what interval is the function decreasing?\n| x | f(x)= - 0.1x² | (x,y) |\n| - 2 | - 0.4 | (-2, - 0.4) |\n| - 1 | - 0.1 | (-1, - 0.1) |\n| 0 | 0 | (0,0) |\n| 1 | - 0.1 | (1, - 0.1) |\n| 2 | - 0.4 | (2, - 0.4) |\nthe function f(x) is increasing over the interval x < 0\n(simplify your answer. type an inequality.)\nthe function f(x) is decreasing over the interval \n(simplify your answer. type an inequality.)

Answer

Explanation:

Step1: Analyze the quadratic - function form

The function $f(x)=-0.1x^{2}$ is a quadratic function in the form $y = ax^{2}+bx + c$ where $a=-0.1$, $b = 0$, and $c = 0$. The graph of a quadratic function $y = ax^{2}+bx + c$ is a parabola, and its axis of symmetry is given by the formula $x=-\frac{b}{2a}$. For $f(x)=-0.1x^{2}$, the axis of symmetry is $x = 0$.

Step2: Determine the increasing and decreasing intervals

Since $a=-0.1<0$, the parabola opens down - ward. A parabola that opens downward is increasing to the left of the axis of symmetry and decreasing to the right of the axis of symmetry.

Answer:

$x>0$