Find the Increasing Domain: Analyzing Function Values from -5 to 5

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

Look at consecutive points and check if both x and y values are getting larger. If x goes up and y goes up too, the function is increasing in that interval.

Q: Why does the function stop being increasing at x = 2?

At $ x = 2 $, f(x) = 15, but at $ x = 3 $, f(x) = 4. Since the y-value decreased while x increased, the function is no longer increasing after x = 2.

Q: What's the difference between increasing and decreasing?

Increasing: As x gets bigger, y gets bigger too.Decreasing: As x gets bigger, y gets smaller. Look at x = 2 to x = 5 in this table!

Q: Can a function be increasing in some parts and decreasing in others?

Absolutely! This function increases for $ x and decreases for \( x > 2 $. Many functions change their behavior at different intervals.

Q: Do I need to check every single point?

You need to check the overall trend in each interval. If all consecutive points in an interval show the same increasing or decreasing pattern, then the whole interval has that behavior.

Function Behavior with Value Tables

In which domain is the function increasing?

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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

00:09 From this point the function starts to decrease

00:18 We can deduce from this the domain of increase

00:22 And this is the solution to the question

Step-by-step written solution

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Understand the problem

In which domain is the function increasing?

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 $x < 2$ the X values and Y values increase simultaneously.

Therefore, the function increases in the domain where

$x < 2$

Final Answer

$x<2$

Key Points to Remember

Essential concepts to master this topic

Definition: Function increases when both x-values and y-values increase together
Technique: Compare consecutive points: (-5,7) to (-1,14) shows increasing trend
Check: Verify at x=2: values stop increasing and start decreasing ✓

Common Mistakes

Avoid these frequent errors

Focusing only on y-values without considering direction
Don't just look for higher y-values = missing the x-direction! A function increases only when BOTH x and y move in the same positive direction. Always check that as x increases, y also increases.

Practice Quiz

Test your knowledge with interactive questions

Does the function in the graph decrease throughout?

FAQ

Everything you need to know about this question

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

Look at consecutive points and check if both x and y values are getting larger. If x goes up and y goes up too, the function is increasing in that interval.

Why does the function stop being increasing at x = 2?

At $x = 2$ , f(x) = 15, but at $x = 3$ , f(x) = 4. Since the y-value decreased while x increased, the function is no longer increasing after x = 2.

What's the difference between increasing and decreasing?

Increasing: As x gets bigger, y gets bigger too.
Decreasing: As x gets bigger, y gets smaller. Look at x = 2 to x = 5 in this table!

Can a function be increasing in some parts and decreasing in others?

Absolutely! This function increases for $x < 2$ and decreases for $x > 2$ . Many functions change their behavior at different intervals.

Do I need to check every single point?

You need to check the overall trend in each interval. If all consecutive points in an interval show the same increasing or decreasing pattern, then the whole interval has that behavior.

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