Function Behavior Analysis: Exploring Multiplication by Zero

Question

Determine whether the function is increasing, decreasing, or constant. For each function check your answers with a graph or table.

For each number, multiply by 0.

00:00 Is the function increasing, decreasing or constant?

00:05 Let's draw the function graph

00:12 Let's substitute X values and find the corresponding Y values

00:36 We can see that Y values are always equal, therefore the function is constant

00:42 And this is the solution to the question

The function is:

$f(x)=x\times0$

Let's start by assuming that x equals 0:

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

Now let's assume that x equals 1:

$f(1)=1\times0=0$

Now let's assume that x equals -1:

$f(-1)=(-1)\times0=0$

Now let's assume that x equals 2:

$f(2)=2\times0=0$

Let's plot all the points on the function's graph:

We can see that the function we obtained is a constant function.

Constant