Finding Decreasing Intervals: Analyzing Function Values from -2 to 10

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

Look at the function values f(x) as you move from left to right. If f(x) gets smaller while x gets larger, the function is decreasing in that interval.

Q: What's the difference between x 2?

For x , check values before x = 2. From the table: f(-2) = 10, f(-1.5) = 8, f(-1) = 6, f(0) = 4, f(2) = 3. The function values are decreasing!

Q: Why isn't x < 5 correct if the function decreases there too?

While the function decreases from x = -2 to x = 2, it increases from x = 2 to x = 3 (f(2) = 3, f(3) = 5). So x

Q: Do I need to check every single point?

Yes! Look at consecutive pairs of points to see the pattern. If any pair shows f(x) increasing as x increases, then that interval is not decreasing.

Q: What if the function has the same value at two points?

If f(x) stays the same as x increases, the function is constant (neither increasing nor decreasing) in that interval.

Function Behavior with Value Tables

In which domain does the function decrease?

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Step-by-step video solution

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00:00 Find the domain of decrease of the function

00:04 The function decreases when X values increase and Y values decrease

00:11 From this point the function starts to increase

00:19 We can deduce from this the domain of decrease

00:28 And this is the solution to the question

Step-by-step written solution

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Understand the problem

In which domain does the function decrease?

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.

According to the value table, we can see that in the domain $x < 2$ , the $x$ values are increasing while the $y$ values are decreasing simultaneously. Therefore, the function is decreasing in the domain $x < 2$ .

Final Answer

$x<2$

Key Points to Remember

Essential concepts to master this topic

Definition: Function decreases when x increases while f(x) decreases
Technique: Compare consecutive points: x = -2 to 2, f(x) goes 10→3
Check: Verify all x-intervals show decreasing pattern consistently ✓

Common Mistakes

Avoid these frequent errors

Confusing x-values with y-values when determining function behavior
Don't look at whether x-values are decreasing = wrong focus! This ignores the actual function output. Always compare how f(x) changes as x increases from left to right.

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 decreasing from a table?

Look at the function values f(x) as you move from left to right. If f(x) gets smaller while x gets larger, the function is decreasing in that interval.

What's the difference between x < 2 and x > 2?

For x < 2, check values before x = 2. From the table: f(-2) = 10, f(-1.5) = 8, f(-1) = 6, f(0) = 4, f(2) = 3. The function values are decreasing!

Why isn't x < 5 correct if the function decreases there too?

While the function decreases from x = -2 to x = 2, it increases from x = 2 to x = 3 (f(2) = 3, f(3) = 5). So x < 5 includes both decreasing AND increasing parts.

Do I need to check every single point?

Yes! Look at consecutive pairs of points to see the pattern. If any pair shows f(x) increasing as x increases, then that interval is not decreasing.

What if the function has the same value at two points?

If f(x) stays the same as x increases, the function is constant (neither increasing nor decreasing) in that interval.

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