Finding Increasing Intervals: Function Analysis with Vertical Line x=0.6

Q: What does it mean for a function to be increasing?

A function is increasing when the y-values get larger as the x-values get larger. Think of it like climbing uphill as you move from left to right on the graph!

Q: Why is the purple line at x = 0.6 important?

The purple line marks a critical point where the function's behavior changes. It helps us identify exactly where the function stops increasing and starts decreasing.

Function Behavior with Reference Lines

In what interval is the function increasing?

Purple line: $x=0.6$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's find where the function is increasing.

00:09 The function increases as both X and Y values go up together.

00:15 It continues to increase until we reach the purple line.

00:19 This area is the domain where our function increases.

00:24 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

In what interval is the function increasing?

Purple line: $x=0.6$

Step-by-step solution

Let's remember that a function is described as 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.

In the graph, we can see that in the domain $x < 0.6$ the function is increasing, meaning the Y values are increasing.

Final Answer

$x<0.6$

Key Points to Remember

Essential concepts to master this topic

Definition: Function increases when y-values rise as x-values increase
Technique: Check slope direction: left of $x = 0.6$ goes upward
Check: Trace curve from left to right: rising = increasing ✓

Common Mistakes

Avoid these frequent errors

Confusing increasing direction with reference line position
Don't think the function increases where $x > 0.6$ just because 0.6 is the reference = wrong interval! The graph shows the function actually decreases after x = 0.6. Always trace the curve's direction, not the reference line's position.

Practice Quiz

Test your knowledge with interactive questions

Is the function in the graph decreasing?

FAQ

Everything you need to know about this question

What does it mean for a function to be increasing?

A function is increasing when the y-values get larger as the x-values get larger. Think of it like climbing uphill as you move from left to right on the graph!

Why is the purple line at x = 0.6 important?

The purple line marks a critical point where the function's behavior changes. It helps us identify exactly where the function stops increasing and starts decreasing.

How do I read the graph to find increasing intervals?

Start from the left and move right along the curve. When the curve is going upward, the function is increasing. When it goes downward, it's decreasing.

Can a function be increasing in multiple intervals?

Yes! A function can increase in some intervals and decrease in others. That's why we need to examine the entire graph and identify each section separately.

What if the function is flat (horizontal)?

When a function is horizontal, it's neither increasing nor decreasing - it's constant. The y-values stay the same as x-values change.

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