Examples with solutions for Increasing and Decreasing Intervals of a Function: Finding Increasing or Decreasing Domains

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 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 #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 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 #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

In what domain does the function increase?

Green line:
x=0.8 x=-0.8

–2–2–2222222000

Video Solution

Step-by-Step Solution

The function increases if X values and Y values increase simultaneously.
In this function, despite its unusual form, we can see that the function continues to increase according to the definition at all times,
and there is no stage where the function decreases.
Therefore, we can say that the function increases for all X, there is no X we can input where the function will be decreasing.

Answer

All values of x x

Exercise #7

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 #8

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 #9

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 #10

In which field does the function decrease?

Green line x=0.45 x=-0.45

Blue line x=0.45 x=0.45

–2–2–2–1–1–1111222333–1–1–1111000

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 -0.45 < x < 0.45 meaning the Y values are increasing.

Answer

0.45 > x > -0.45

Exercise #11

In which domain is the function increasing?

f(x)x-57-1.58-110014215343.5250

Video Solution

Step-by-Step Solution

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

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

According to the given value table, we can see that in the domain where x < 2 the X values and Y values increase simultaneously.

Therefore, the function increases in the domain where

x < 2

Answer

x<2

Exercise #12

In which domain does the function decrease?

f(x)x-24-110011721151671911

Video Solution

Step-by-Step Solution

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

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

According to the given value table, we can see that in the domain where x < 0 X values increase and Y values decrease simultaneously.

Therefore, the function decreases in the domain where

x < 0

Answer

x<0

Exercise #13

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

Exercise #14

In which domain is the function increasing?

f(x)x-44-1100116210014-78-9

Video Solution

Step-by-Step Solution

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

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

According to the given value table, we can see that in the domain where 10 > x > 0 the X values and Y values increase simultaneously.

Therefore, the function increases in the domain where

10 > x > 0

Answer

10 > x > 0

Exercise #15

In which domain is the function increasing?

f(x)x-210-1.58-0.560021353.5759

Video Solution

Step-by-Step Solution

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

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

According to the given value table, we can see that in the domain where x > 0 the X values and Y values increase simultaneously.

Therefore, the function increases in the domain where

x > 0

Answer

x>0

Exercise #16

In which domain does the function decrease?

f(x)x001223354352607-4

Video Solution

Step-by-Step Solution

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

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

According to the given value table, we can see that in the domain where x > 3 X values increase and Y values decrease simultaneously.

Therefore, the function decreases in the domain where

x > 3

Answer

x>3

Exercise #17

In which domain is the function increasing?

f(x)x-104-48-211010213-54-75-9

Video Solution

Step-by-Step Solution

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

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

According to the given value table, we can see that in the domain where x < -2 the X values and Y values increase simultaneously.

Therefore, the function increases in the domain where

x < -2

Answer

x<-2

Exercise #18

In which domain is the function increasing?

f(x)x-54-11102-14-25-57-78-9

Video Solution

Step-by-Step Solution

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

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

According to our given value table, we can see that X values increase while Y values decrease simultaneously.

Therefore, the function decreases throughout its domain, and there is no domain where it increases.

Answer

No upward dominance

Exercise #19

In which domain is the function increasing?

x-1010-78-360425463.5789

Video Solution

Step-by-Step Solution

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

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

According to the given value table, we can see that in the domain where 0 > x X values and Y values increase simultaneously.

Therefore, the function increases in the domain where

x > 0

Answer

x>0

Exercise #20

In which domain is the function increasing?

x-24-1100111.52305-78-9

Video Solution

Step-by-Step Solution

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

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

According to the given value table, we can see that in the domain where 1.5 > x > 0 the X values and Y values increase simultaneously.

Therefore, the function increases in the domain where

1.5 > x > 0

Answer

1.5>x>0