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

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.

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

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).

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.

Choose the graph that best represents the following:

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

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.

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 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:

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

In what domain does the function increase?

x > 0

In what domain is the function negative?

x > 1

In what domain is the function increasing?

Entire$x$

In what domain does the function increase?

x<0 $$

In what interval is the function increasing?

Purple line: $x=0.6$

x<0.6

In what domain does the function increase?

Green line:
$x=-0.8$

All values of $x$

In which interval does the function decrease?

Red line: $x=0.65$

All values of $x$

In which interval does the function decrease?

Red line: $x=1.3$

1.3 > x > -1.3

In what domain does the function increase?

Black line: $x=1.1$

1.1 > x > 0