Finding Increasing Domains: Analyzing Function Values from -5 to 8

Function Analysis with Decreasing Behavior

In which domain is the function increasing?

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the domain where the function increases
00:03 The function increases when X and Y values increase simultaneously
00:08 It seems that the function is constantly decreasing
00:16 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-54-11102-14-25-57-78-9

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 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.

3

Final Answer

No upward dominance

Key Points to Remember

Essential concepts to master this topic
  • Increasing Function: Both x-values and y-values increase together simultaneously
  • Analysis Technique: Compare consecutive points: (-5,4) to (-1,1) shows decrease
  • Verification: Check all intervals show y decreasing as x increases ✓

Common Mistakes

Avoid these frequent errors
  • Confusing positive y-values with increasing function
    Don't think f(x) = 4 means increasing because 4 is positive! Function behavior depends on how y-values change as x increases, not whether y-values are positive. Always compare consecutive points to see if y-values rise or fall as x increases.

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

What's the difference between increasing and positive function values?

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A function is increasing when y-values get larger as x-values get larger. Positive function values just means f(x) > 0. A function can have positive values but still be decreasing!

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

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Look at consecutive points in order. If the y-values get bigger as the x-values get bigger, it's increasing. In our table: 4 → 1 → 0 → -1 → -2 → -5 → -7 → -9 (all decreasing!).

Can a function be increasing in some parts but not others?

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Yes! Functions can be increasing in some intervals and decreasing in others. That's why we look for domains where the function increases, not the whole function.

What does 'no upward dominance' mean?

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'No upward dominance' means there's no interval where the function consistently goes up. Since our function only decreases (goes down), there's no domain where it increases.

Why isn't the answer 'All x' if we can see the whole table?

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The answer would be 'All x' only if the function was increasing everywhere. Our function decreases at every interval, so it's never increasing anywhere!

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