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.

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 Decreasing Interval of a function

Examples with solutions for Decreasing Interval of a function

Exercise #1

In what domain does the function increase?

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

Video Solution

Step-by-Step Solution

Let's remember that the function increases if the X values and Y values increase simultaneously.

On the other hand, the function decreases if the X values increase and the Y values decrease simultaneously.

In the given graph, we notice that the function increases in the domain where x > 0 meaning the Y values are increasing.

Answer

x > 0

Exercise #2

In what domain does the function increase?

000

Video Solution

Step-by-Step Solution

Let's remember that the function increases if the X values and Y values increase simultaneously.

On the other hand, the function decreases if the X values increase and the Y values decrease simultaneously.

In the given graph, we notice that the function increases in the domain where x < 0 meaning the Y values are increasing.

Answer

x<0

Exercise #3

In what domain is the function increasing?

–5–5–5555101010151515–5–5–5555000

Video Solution

Step-by-Step Solution

Let's remember that a function is increasing if both X values and Y values are increasing simultaneously.

A function is decreasing if X values are increasing while Y values are decreasing simultaneously.

In the graph shown, we can see that the function is increasing in every domain, therefore the function is increasing for all X.

Answer

Entirex x

Exercise #4

In what domain is the function negative?

–0.5–0.5–0.50.50.50.51111.51.51.5222000

Video Solution

Step-by-Step Solution

Let's remember that a function is increasing if both X values and Y values are increasing simultaneously.

A function is decreasing if X values are increasing while Y values are decreasing simultaneously.

In the graph, we can see that in the domain x > 1 the function is decreasing, meaning the Y values are decreasing.

Answer

x > 1

Exercise #5

In what interval is the function increasing?

Purple line: x=0.6 x=0.6

111222333111000

Video Solution

Step-by-Step Solution

Let's remember that a function is increasing if both X values and Y values are increasing simultaneously.

A function is decreasing if X values are increasing while Y values are decreasing simultaneously.

In the graph, we can see that in the domain x < 0.6 the function is increasing, meaning the Y values are increasing.

Answer

x<0.6

Exercise #6

Determine the domain of the following function:

A function describing the charging of a computer battery during use.

Step-by-Step Solution

According to logic, the computer's battery during use will always decrease since the battery serves as an energy source for the computer.

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

Answer

Always decreasing

Exercise #7

Determine the domain of the following function:

The function describes a student's grades throughout the year.

Step-by-Step Solution

According to logic, the student's grades throughout the year depend on many criteria that are not given to us.

Therefore, the appropriate domain for the function is - it is impossible to know.

Answer

Impossible to know.

Exercise #8

Determine the domain of the following function:

The function represents the weight of a person over a period of 3 years.

Step-by-Step Solution

Logically, a person's weight is something that fluctuates.

In one week, a person's weight can increase, but in the following week, it can decrease.

Therefore, the domain that suits this function is - partly increasing and partly decreasing.

Answer

Partly increasing and partly decreasing.

Exercise #9

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 #10

Determine which domain corresponds to the function described below:

The function represents the height of a child from birth to first grade.

Step-by-Step Solution

According to logic, a child's height from birth until first grade will always be increasing as the child grows.

Therefore, the domain that suits this function is - always increasing.

Answer

Always increasing.

Exercise #11

In which interval does the function decrease?

Red line: x=0.65 x=0.65

111222333–1–1–1111000

Video Solution

Step-by-Step Solution

Remember that a function is increasing if both X values and Y values are increasing simultaneously.

A function is decreasing if X values are increasing while Y values are decreasing simultaneously.

In the plotted graph, we can see that the function is decreasing in all domains. In other words, it is decreasing for all X.

Answer

All values of x x

Exercise #12

In what domain does the function increase?

Black line: x=1.1 x=1.1

–2–2–2222444666222000

Video Solution

Step-by-Step Solution

Remember that a function is increasing if the X values and Y values are increasing simultaneously.

A function is decreasing if the X values are increasing and the Y values are decreasing simultaneously.

In the plotted graph, we can see that in the domain 1.1 > x > 0 the function is increasing, meaning the Y values are increasing.

Answer

1.1 > x > 0

Exercise #13

Which domain corresponds to the described function:

The function represents the velocity of a stone after being dropped from a great height as a function of time.

Step-by-Step Solution

According to logic, the speed of the stone during a fall from a great height will increase as it falls with acceleration.

In other words, the speed of the stone increases, so the appropriate domain for this function is - always increasing.

Answer

Always increasing

Exercise #14

In what domain does the function increase?

–10–10–10–5–5–5555101010151515202020–10–10–10–5–5–5555000

Video Solution

Step-by-Step Solution

Let's remember that the function increases if the X values and Y values increase simultaneously.

On the other hand, the function decreases if the X values increase and the Y values decrease simultaneously.

In the given graph, we notice that the function increases in the domain where 1 > x > -1 meaning the Y values are increasing.

Answer

1 > x > -1

Exercise #15

In which domain does the function decrease?

f(x)x-210-1.58-160423353.57109

Video Solution

Step-by-Step Solution

Let's remember that a function is increasing if both X values and Y values are increasing simultaneously.

A function is decreasing if X values are increasing while Y values are decreasing simultaneously.

According to the value table, we can see that in the domain x < 2 , X values are increasing while Y values are decreasing simultaneously. Therefore, the function is decreasing in the domain x < 2

Answer

x<2

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. Increasing Intervals of a function
  7. Domain of a Function
  8. Indefinite integral
  9. Inputing Values into a Function