Finding Decreasing Intervals: Analyzing f(x) Value Table from 0 to 7

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

Look for intervals where x values increase while f(x) values decrease at the same time. Both conditions must happen together!

Q: What does x > 3 mean exactly?

This means all x values greater than 3 in our table: x=4, x=5, x=6, and x=7. In this entire interval, f(x) consistently decreases from 5→3→2→0→(-4).

Q: Could the answer be x < 3 instead?

No! From x=0 to x=3, f(x) increases from 0 to 5. The function is increasing in this interval, not decreasing.

Q: How do I check my answer?

List the points where $ x > 3 $: (4,3), (5,2), (6,0), (7,-4). Notice f(x) keeps getting smaller: 3→2→0→(-4) ✓

Function Behavior with Value Tables

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

00:03 Let's find where our function goes down.

00:06 The function decreases when X goes up and Y goes down. Notice the trend.

00:13 At this point, watch closely as the function begins to decline.

00:23 From here, we can determine where the function is decreasing.

00:32 And that's the solution to our problem!

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 $x > 3$ X values increase and Y values decrease simultaneously.

Therefore, the function decreases in the domain where

$x > 3$

Final Answer

$x>3$

Key Points to Remember

Essential concepts to master this topic

Rule: Function decreases when x increases while f(x) decreases
Technique: Compare consecutive points: from x=3 to x=4, f(x) goes 5→3
Check: Verify all intervals where f(x) drops as x increases ✓

Common Mistakes

Avoid these frequent errors

Confusing increasing and decreasing behavior
Don't look only at f(x) values going down = wrong domain! This ignores that x must also be increasing. Always check that both x increases AND f(x) decreases simultaneously in the same 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 decreasing from a table?

Look for intervals where x values increase while f(x) values decrease at the same time. Both conditions must happen together!

Why isn't the function decreasing from x=0 to x=3?

Even though there are some drops in f(x), the overall trend from x=0 to x=3 shows f(x) going from 0→2→3→5, which is increasing overall.

What does x > 3 mean exactly?

This means all x values greater than 3 in our table: x=4, x=5, x=6, and x=7. In this entire interval, f(x) consistently decreases from 5→3→2→0→(-4).

Could the answer be x < 3 instead?

No! From x=0 to x=3, f(x) increases from 0 to 5. The function is increasing in this interval, not decreasing.

How do I check my answer?

List the points where $x > 3$ : (4,3), (5,2), (6,0), (7,-4). Notice f(x) keeps getting smaller: 3→2→0→(-4) ✓

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