# Increasing and Decreasing Intervals of a Function - Examples, Exercises and Solutions

The intervals where the function is increasing show a certain situation in which the values of $X$ and $Y$ increase together.

The intervals where the function is decreasing expose a certain situation in which the value of $X$ in a function increases while that of $Y$ decreases.

## Practice Increasing and Decreasing Intervals 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 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 #3

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 #4

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

### Exercise #5

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 #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$(-1)$.

### 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 #2

In what domain does the function increase?

x > 0

### Exercise #3

In what domain is the function negative?

x > 1

### Exercise #4

In what domain is the function increasing?

### Video Solution

Entire$x$

### Exercise #5

In what domain does the function increase?

x<0 

### Exercise #1

In what interval is the function increasing?

Purple line: $x=0.6$

x<0.6

### Exercise #2

In what domain does the function increase?

Green line:
$x=-0.8$

### Video Solution

All values of $x$

### Exercise #3

In which interval does the function decrease?

Red line: $x=0.65$

### Video Solution

All values of $x$

### Exercise #4

In which interval does the function decrease?

Red line: $x=1.3$

1.3 > x > -1.3

### Exercise #5

In what domain does the function increase?

Black line: $x=1.1$