The increasing intervals of a function

The increasing intervals of a function

An increasing interval of a function expresses the same values of X (the interval), in which the values of the function (Y) grow parallel to the growth of the values of X to the right.

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

Question 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.

Question 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).

Question 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).

Question 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 \( (-1) \).

Question 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.

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 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.

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.

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. 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

Question 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\( (-1) \).

Question 2

In what domain does the function increase?

Question 3

In what domain is the function negative?

Question 4

In what domain is the function increasing?

Question 5

In what domain does the function increase?

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

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

Question 1

In what interval is the function increasing?

Purple line: \( x=0.6 \)

Question 2

In what domain does the function increase?

Green line:

\( x=-0.8 \)

Question 3

In which interval does the function decrease?

Red line: \( x=0.65 \)

Question 4

In which interval does the function decrease?

Red line: \( x=1.3 \)

Question 5

In what domain does the function increase?

Black line: \( x=1.1 \)

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