Function Domain Analysis: Finding Increasing Intervals in [-10, 5]

Function Analysis with Table Values

In which domain is the function increasing?

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the domain of increase of the function
00:03 The function increases when X and Y values increase simultaneously
00:11 At this point the function starts to decrease
00:24 We can deduce from this the domain of increase
00:30 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

In which domain is the function increasing?

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

2

Step-by-step solution

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 wherex<2 x < -2 the X values and Y values increase simultaneously.

Therefore, the function increases in the domain where

x<2 x < -2

3

Final Answer

x<2 x<-2

Key Points to Remember

Essential concepts to master this topic
  • Increasing Function: Y-values increase as X-values increase together
  • Technique: Compare consecutive points: X from -10 to -4, Y from 4 to 8
  • Check: Verify all intervals where both X and Y rise simultaneously ✓

Common Mistakes

Avoid these frequent errors
  • Looking at Y-values alone without considering X-direction
    Don't just find where Y-values are positive or large = wrong intervals! This ignores the direction of change. Always check if both X and Y increase together in the same interval.

Practice Quiz

Test your knowledge with interactive questions

Is the function in the graph decreasing? yx

FAQ

Everything you need to know about this question

How do I tell if a function is increasing from a table?

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Look at consecutive points! If both X and Y values go up together, the function is increasing in that interval. For example: from X = -10 to X = -4, Y goes from 4 to 8.

Why is the answer x<2 x < -2 and not the other intervals?

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From the table, Y-values only increase consistently when X goes from -10 to -2. After X = -2, the Y-values start decreasing (from 11 to 10 to 1), so the function stops being increasing.

What does it mean when the function decreases?

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A function decreases when X-values increase but Y-values go down. In this table, from X = -2 to X = 5, Y drops from 11 down to -9.

Can a function be both increasing and decreasing?

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Yes! Functions can increase in some intervals and decrease in others. That's why we specify where (the domain) the function has each behavior.

Do I need to check every single point in the table?

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Yes, check consecutive pairs of points! Compare (X₁, Y₁) with (X₂, Y₂) to see if both X and Y increase together. This helps you find the exact intervals.

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