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)=0.4x² | (x,y) |\n| -2 | 1.6 | (-2,1.6) |\n| -1 | 0.4 | (-1,0.4) |\n| 0 | 0 | (0,0) |\n| 1 | 0.4 | (1,0.4) |\n| 2 | 1.6 | (2,1.6) |\nthe function f(x) is increasing 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)=0.4x² | (x,y) |\n| -2 | 1.6 | (-2,1.6) |\n| -1 | 0.4 | (-1,0.4) |\n| 0 | 0 | (0,0) |\n| 1 | 0.4 | (1,0.4) |\n| 2 | 1.6 | (2,1.6) |\nthe function f(x) is increasing over the interval \n(simplify your answer. type an inequality.)

Answer

Explanation:

Step1: Recall the property of quadratic function

The function $f(x)=0.4x^{2}$ is a quadratic - function in the form $y = ax^{2}+bx + c$ with $a = 0.4$, $b = 0$, 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 $x=-\frac{b}{2a}$.

Step2: Calculate the axis of symmetry

Substitute $a = 0.4$ and $b = 0$ into the axis - of - symmetry formula $x=-\frac{b}{2a}$. We get $x =-\frac{0}{2\times0.4}=0$.

Step3: Determine the increasing and decreasing intervals

Since $a = 0.4>0$, the parabola opens upward. A parabola that opens upward is decreasing on the left - hand side of the axis of symmetry and increasing on the right - hand side of the axis of symmetry. So the function $f(x)$ is increasing for $x\geq0$.

Answer:

$x\geq0$