Function Behavior Analysis: Effects of Constant Multiplication

Question

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

Each number is multiplied by the same number.

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

00:03 Let's draw the function graph

00:13 Let's substitute X values and find the corresponding Y values

00:40 Now let's substitute negative X values to check the left side of the graph

01:02 We can see that the graph decreases until the origin and then increases

01:10 And this is the solution to the question

The function is:

$f(x)=x^2$

Let's start with x equal to 0:

$f(0)=0^2=0$

Now let's assume x is equal to 1:

$f(1)=1^2=1$

Now let's assume x is equal to 2:

$f(2)=2^2=4$

Now let's assume x is equal to -1:

$f(-1)=(-1)^2=1$

Now let's assume x is equal to -2:

$f(-2)=(-2)^2=4$

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

We can see that we have a function that is both increasing and decreasing.

Increasing and decreasing