Find the Decreasing Domain: Analyzing Function f(x) from -2 to 19

Q: How do I tell if a function is increasing or decreasing from a table?

Look at consecutive points! If y-values get bigger as x-values increase, the function is increasing. If y-values get smaller as x-values increase, it's decreasing.

Q: Why is the answer x < 0 and not just 'from -2 to 0'?

The notation \( x describes the domain condition where decreasing occurs. Since we only see data from x = -2 to x = 19, we can only confirm decreasing behavior for x based on this table.

Q: What if the function goes up and down in different parts?

That's normal! Functions can have multiple intervals where they increase and decrease. You need to identify all intervals where the specific behavior (increasing or decreasing) occurs.

Q: Can I use this method for any function table?

Yes! This comparison method works for any table of values. Just remember to check consecutive points and look at the relationship between x and y changes.

Q: What does it mean that y goes from 4 to 1 to 0?

This shows the function is decreasing in that interval! As x increases from -2 to -1 to 0, the corresponding y-values are getting smaller: 4 → 1 → 0.

Function Behavior with Tabular Analysis

In which domain does the function decrease?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the domain of decrease of the function

00:03 The function decreases when X values increase and Y values decrease

00:07 From this point the function begins to increase

00:18 We'll deduce from this the domain of decrease

00:25 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

In which domain does the function decrease?

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 where $x < 0$ X values increase and Y values decrease simultaneously.

Therefore, the function decreases in the domain where

$x < 0$

Final Answer

$x<0$

Key Points to Remember

Essential concepts to master this topic

Rule: Function decreases when x increases and y decreases simultaneously
Technique: Compare consecutive points: from x=-2 to x=0, y goes 4→1→0
Check: Verify all intervals where y-values drop as x-values rise ✓

Common Mistakes

Avoid these frequent errors

Confusing increasing and decreasing behavior
Don't look at just one coordinate changing = wrong interpretation! Students often think decreasing means x < 0 or y < 0, but it's about the relationship. Always check if y-values drop while x-values increase in that interval.

Practice Quiz

Test your knowledge with interactive questions

Is the function in the graph decreasing?

FAQ

Everything you need to know about this question

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

Look at consecutive points! If y-values get bigger as x-values increase, the function is increasing. If y-values get smaller as x-values increase, it's decreasing.

Why is the answer x < 0 and not just 'from -2 to 0'?

The notation $x < 0$ describes the domain condition where decreasing occurs. Since we only see data from x = -2 to x = 19, we can only confirm decreasing behavior for x < 0 based on this table.

What if the function goes up and down in different parts?

That's normal! Functions can have multiple intervals where they increase and decrease. You need to identify all intervals where the specific behavior (increasing or decreasing) occurs.

Can I use this method for any function table?

Yes! This comparison method works for any table of values. Just remember to check consecutive points and look at the relationship between x and y changes.

What does it mean that y goes from 4 to 1 to 0?

This shows the function is decreasing in that interval! As x increases from -2 to -1 to 0, the corresponding y-values are getting smaller: 4 → 1 → 0.

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