Increasing Intervals of a function - Examples, Exercises and Solutions

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.

Suggested Topics to Practice in Advance

  1. Ways to represent a function
  2. Representing a Function Verbally and with Tables
  3. Graphical Representation of a Function
  4. Algebraic Representation of a Function
  5. Notation of a Function
  6. Rate of Change of a Function
  7. Variation of a Function
  8. Rate of change represented with steps in the graph of the function
  9. Rate of change of a function represented graphically
  10. Constant Rate of Change
  11. Variable Rate of Change
  12. Rate of Change of a Function Represented by a Table of Values

Practice Increasing 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.

Answer

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.

Answer

WeatherTemperature'000

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.

Answer

Weather101010Speed

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) (-1) .

Video Solution

Step-by-Step Solution

The function is:

f(x)=x1 f(x)=\frac{x}{-1}

Let's start by assuming that x equals 0:

f(0)=01=0 f(0)=\frac{0}{-1}=0

Now let's assume that x equals 1:

f(1)=11=1 f(1)=\frac{1}{-1}=-1

Now let's assume that x equals 2:

f(1)=11=1 f(-1)=\frac{-1}{-1}=1

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

–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666–1–1–1111222333444000

We see that we got a decreasing function.

Answer

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.

Video Solution

Step-by-Step Solution

The function is:

f(x)=x×0 f(x)=x\times0

Let's start by assuming that x equals 0:

f(0)=0×0=0 f(0)=0\times0=0

Now let's assume that x equals 1:

f(1)=1×0=0 f(1)=1\times0=0

Now let's assume that x equals -1:

f(1)=(1)×0=0 f(-1)=(-1)\times0=0

Now let's assume that x equals 2:

f(2)=2×0=0 f(2)=2\times0=0

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

–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666–3–3–3–2–2–2–1–1–1111222000

We can see that the function we obtained is a constant function.

Answer

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) (-1) .

Video Solution

Step-by-Step Solution

The function is:

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

Let's start by assuming that x equals 0:

f(0)=(1)×0=0 f(0)=(-1)\times0=0

Now let's assume that x equals minus 1:

f(1)=(1)×(1)=1 f(-1)=(-1)\times(-1)=1

Now let's assume that x equals 1:

f(1)=(1)×1=1 f(1)=(-1)\times1=-1

Now let's assume that x equals 2:

f(2)=(1)×2=2 f(2)=(-1)\times2=-2

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

–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666–3–3–3–2–2–2–1–1–1111222000

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

Answer

Decreasing

Exercise #2

In what domain does the function increase?

–20–20–20–10–10–10101010202020–10–10–10101010000

Video Solution

Answer

x > 0

Exercise #3

In what domain is the function negative?

–0.5–0.5–0.50.50.50.51111.51.51.5222000

Video Solution

Answer

x > 1

Exercise #4

In what domain is the function increasing?

–5–5–5555101010151515–5–5–5555000

Video Solution

Answer

Entirex x

Exercise #5

In what domain does the function increase?

000

Video Solution

Answer

x<0

Exercise #1

In what interval is the function increasing?

Purple line: x=0.6 x=0.6

111222333111000

Video Solution

Answer

x<0.6

Exercise #2

In what domain does the function increase?

Green line:
x=0.8 x=-0.8

–2–2–2222222000

Video Solution

Answer

All values of x x

Exercise #3

In which interval does the function decrease?

Red line: x=0.65 x=0.65

111222333–1–1–1111000

Video Solution

Answer

All values of x x

Exercise #4

In which interval does the function decrease?

Red line: x=1.3 x=1.3

–4–4–4–2–2–2222444666888101010–2–2–2222444000

Video Solution

Answer

1.3 > x > -1.3

Exercise #5

In what domain does the function increase?

Black line: x=1.1 x=1.1

–2–2–2222444666222000

Video Solution

Answer

1.1 > x > 0

Topics learned in later sections

  1. Functions for Seventh Grade
  2. Increasing and Decreasing Intervals (Functions)
  3. Increasing functions
  4. Decreasing function
  5. Constant Function
  6. Decreasing Interval of a function
  7. Domain of a Function
  8. Indefinite integral
  9. Inputing Values into a Function