Increasing and Decreasing Intervals of a Function: Identifying increase and decrease from a verbal description of the function

Determine whether the function is increasing, decreasing, or constant. For each function check your answers using a graph or a table. Each number is multiplied by itself three times.

The function is:

$f(x)=xxx$

Let's start with x equal to 0:

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

Now let's assume x is equal to 1:

$f(1)=1\times1\times1=1$

Now let's assume x is equal to 2:

$f(2)=2\times2\times2=8$

Let's record all the data in a table:

Note that the function is always increasing.

Growing

Determine whether the function is increasing, decreasing, or constant. For each function, check your answers using a graph or a table:
Each number is multiplied by 0.5.

The function is:

$f(x)=0.5x$

Let's start with x equal to 0:

$f(0)=0\times0.5=0$

Now let's assume x is equal to 1:

$f(1)=1\times0.5=0.5$

Now let's assume x is equal to 2:

$f(2)=2\times0.5=1$

Let's record all the data in a table:

Note that the function is always increasing.

Growing

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

Each number is multiplied by the same number with different signs

The function is:

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

Let's start by assuming x equals 0:

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

Now let's assume x equals 1:

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

Now let's assume x equals minus 1:

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

Now let's assume x equals 2:

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

Now let's assume x equals minus 2:

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

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

We can see that the function we obtained rises and falls.

Increasing and decreasing

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.

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

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$(-1)$.

The function is:

$f(x)=(-1)x$

Let's start by assuming that x equals 0:

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

Now let's assume that x equals minus 1:

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

Now let's assume that x equals 1:

$f(1)=(-1)\times1=-1$

Now let's assume that x equals 2:

$f(2)=(-1)\times2=-2$

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

We can see that the function we got is a decreasing function.

Decreasing

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

Each number is multiplied by the same number.

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 minus 1:

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

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

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

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

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

Increasing and decreasing

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

Each number is divided by $(-1)$.

The function is:

$f(x)=\frac{x}{-1}$

Let's start by assuming that x equals 0:

$f(0)=\frac{0}{-1}=0$

Now let's assume that x equals 1:

$f(1)=\frac{1}{-1}=-1$

Now let's assume that x equals 2:

$f(-1)=\frac{-1}{-1}=1$

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

We see that we got a decreasing function.

Decreasing

Determine whether the function is increasing, decreasing, or constant. Check your answer with a graph or table.

For each number corresponding to the number $-1$.

The function is:

$f(x)=x-1$

Let's start with x equal to 0:

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

Now let's assume x is equal to 1:

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

Now let's assume x is equal to 2:

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

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

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

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

It appears that the function we obtained is an increasing function.

Increasing