# Decreasing Interval of a function - Examples, Exercises and Solutions

The decreasing intervals of a function

A decreasing interval of a function expresses the same values of X (the interval), in which the values of the function (Y) decrease parallelly to the increase of the values of X to the right.

In certain cases, the decreasing interval begins at the maximum point, but it does not necessarily have to be this way.

## examples with solutions for decreasing interval of a function

### Exercise #1

Determine which domain corresponds to the function described below:

The function represents the amount of fuel in a car's tank according to the distance traveled by the car.

### Step-by-Step Solution

According to the definition, the amount of fuel in the car's tank will always decrease, since during the trip the car consumes fuel in order to travel.

Therefore, the domain that is suitable for this function is - always decreasing.

Always decreasing

### Exercise #2

Choose the graph that best describes the following:

The acceleration of a ball (Y) after throwing it from a building as a function of time (X).

### Step-by-Step Solution

Since acceleration is dependent on time, it will be constant.

The force of gravity on Earth is constant, meaning the velocity of Earth's gravity is constant and therefore the graph will be straight.

The graph that appears in answer B satisfies this.

### Exercise #3

Choose the graph that best represents the following:

Temperature of lukewarm water (Y) after placing in the freezer as a function of time (X).

### Step-by-Step Solution

Since the freezing point of water is below 0, the temperature of the water must drop below 0.

The graph in answer B describes a decreasing function and therefore this is the correct answer.

### Exercise #4

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$(-1)$.

### Step-by-Step Solution

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

### Exercise #5

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 $(-1)$.

### Step-by-Step Solution

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

## examples with solutions for decreasing interval of a function

### Exercise #1

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.

### Step-by-Step Solution

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

### Exercise #2

In what interval is the function increasing?

Purple line: $x=0.6$

x<0.6

### Exercise #3

In what domain does the function increase?

x > 0

### Exercise #4

In what domain is the function negative?

x > 1

### Exercise #5

In what domain is the function increasing?

### Video Solution

Entire$x$

## examples with solutions for decreasing interval of a function

### Exercise #1

In what domain does the function increase?

x<0 

### Exercise #2

In what domain does the function increase?

Black line: $x=1.1$

1.1 > x > 0

### Exercise #3

In which interval does the function decrease?

Red line: $x=1.3$

1.3 > x > -1.3

### Exercise #4

In what domain does the function increase?

Green line:
$x=-0.8$

### Video Solution

All values of $x$

### Exercise #5

In which interval does the function decrease?

Red line: $x=0.65$

### Video Solution

All values of $x$