Finding Decreasing Intervals: Analyzing Function Behavior from Graph

Q: How do I tell if a function is decreasing just by looking at the graph?

Follow the curve from left to right. If the line or curve is going downward, the function is decreasing in that interval. Think of it like walking downhill!

Q: What's the difference between where a function is negative and where it's decreasing?

Negative values mean y Decreasing means the function slopes downward. A function can be negative but still increasing, or positive but decreasing!

Q: Why does the answer use x < -1 instead of a specific point?

Because decreasing behavior happens over an interval, not just at one point. The function decreases for all x-values less than -1, so we write it as an inequality.

Q: How can I check my answer without the equation?

Pick two points in your interval where \( x . If the point with the larger x-value has a smaller y-value, you're correct!

Q: What if the graph has both increasing and decreasing parts?

That's normal! Many functions change behavior. Look for turning points where the slope changes from positive to negative (or vice versa) to identify different intervals.

Function Behavior with Graphical Analysis

In what domain does the function decrease?

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

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 A function decreases when X values increase and Y values decrease

00:06 We can see that the function decreases until X=-1

00:15 Therefore the domain of decrease will be while X is less than (-1)

00:21 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 what domain does the function decrease?

Step-by-step solution

Let's remember that the function increases if the X values and Y values increase simultaneously.

On the other hand, the function decreases if the X values increase and the Y values decrease simultaneously.

In the graph, we can see that the function decreases in the domain where $x < -1$ , meaning that the Y values are decreasing.

Final Answer

$x<-1$

Key Points to Remember

Essential concepts to master this topic

Decreasing Function: Y-values decrease as X-values increase from left to right
Graph Reading: Look for downward slopes where $x < -1$ shows decreasing behavior
Verification: Check multiple points: as x moves right, y moves down ✓

Common Mistakes

Avoid these frequent errors

Confusing increasing and decreasing intervals
Don't look at where y-values are negative and assume the function is decreasing there = wrong interpretation! A function can have negative y-values but still be increasing. Always focus on the slope direction: if the graph goes downward from left to right, it's decreasing.

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 just by looking at the graph?

Follow the curve from left to right. If the line or curve is going downward, the function is decreasing in that interval. Think of it like walking downhill!

What's the difference between where a function is negative and where it's decreasing?

Negative values mean y < 0 (below the x-axis). Decreasing means the function slopes downward. A function can be negative but still increasing, or positive but decreasing!

Why does the answer use x < -1 instead of a specific point?

Because decreasing behavior happens over an interval, not just at one point. The function decreases for all x-values less than -1, so we write it as an inequality.

How can I check my answer without the equation?

Pick two points in your interval where $x < -1$ . If the point with the larger x-value has a smaller y-value, you're correct!

What if the graph has both increasing and decreasing parts?

That's normal! Many functions change behavior. Look for turning points where the slope changes from positive to negative (or vice versa) to identify different intervals.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Functions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime