Increasing Intervals of a function

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

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Test yourself on increasing and decreasing intervals of a function!

einstein

Does the function in the graph decrease throughout?

YYYXXX

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Examples and exercises with solutions of intervals of increasing functions

Exercise #1

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 #2

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 #3

In what domain is the function increasing?

–5–5–5555101010151515–5–5–5555000

Video Solution

Step-by-Step Solution

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

Conversely, a function is decreasing if the X values are increasing while the Y values are decreasing simultaneously.

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

Answer

All values of x 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

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Question 1

In what domain does the function increase?

000

Question 2

In what domain does the function increase?

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

Question 3

In what domain is the function increasing?

–5–5–5555101010151515–5–5–5555000

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