Analyze Function Behavior: Multiplication with Opposite Signs

Determine whether the function described below is increasing, decreasing, or constant:

Each number is multiplied by the same number with different signs.

The function is:

$f(x)=x\times(-x)$

Let's start by assuming that$x$ equals 0:

$f(0)=0\times0=0$

Now let's assume that $x$ equals 1:

$f(1)=1\times-1=-1$

Now let's assume that $x$ equals -1:

$f(-1)=(-1)\times(-1)=1$

Now let's assume that $x$ equals 2:

$f(2)=2\times(-2)=-4$

Now let's assume that $x$ equals -2:

$f(-2)=(-2)\times(-2)=4$

Finally, let's plot all of the points on a graph:

We can see that the function both increases and decreases.