Function Analysis: Finding Decreasing Intervals Between x=-0.45 and x=0.45

Q: How do I tell if a function is increasing or decreasing?

Follow the curve from left to right. If the curve goes upward, the function is increasing. If it goes downward, it's decreasing.

Q: What does the interval notation mean?

The notation \( -0.45 means we're only looking at x-values between -0.45 and 0.45, not including the endpoints themselves.

Q: Why are there green and blue lines on the graph?

The green line at x = -0.45 and blue line at x = 0.45 mark the boundaries of the interval we need to analyze. They help you focus on the right section of the curve.

Q: What if the function both increases and decreases in the interval?

Look for the overall trend in the given interval. If there are multiple behaviors, the question usually asks for where it's primarily increasing or decreasing.

Q: How can I be sure I'm reading the graph correctly?

Start at the left boundary (x = -0.45) and slowly move your finger to the right boundary (x = 0.45). Watch if your finger moves up (increasing) or down (decreasing).

Function Behavior with Interval Analysis

In which field does the function decrease?

Green line $x=-0.45$

Blue line $x=0.45$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the domain where the function decreases

00:03 The function decreases when X values increase and Y values decrease

00:07 Let's start by finding the domains where the function increases

00:13 The function decreases between the increasing domains of the function

00:18 Let's find the exact start and end points of the decreasing domain

00:26 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 which field does the function decrease?

Green line $x=-0.45$

Blue line $x=0.45$

Step-by-step solution

Let's remember that the function increases if the $x$ and $y$ values increase simultaneously.

On the other hand, the function decreases if the $x$ values increase while the $y$ values decrease simultaneously.

In the given graph, we notice that the function increases in the domain where $-0.45 < x < 0.45$ , meaning the $y$ values are increasing.

Final Answer

$0.45 > x > -0.45$

Key Points to Remember

Essential concepts to master this topic

Decreasing Function: As x increases, y values decrease simultaneously
Reading Graph: Between x = -0.45 and x = 0.45, trace curve from left to right
Check Direction: Function goes down from left to right in given interval ✓

Common Mistakes

Avoid these frequent errors

Confusing increasing and decreasing behavior
Don't assume the function decreases everywhere just because it looks like it goes down somewhere = wrong interval identification! Students often misread which direction the curve actually moves. Always trace the curve from left to right within the specified boundaries to see if y-values are rising or falling.

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 increasing or decreasing?

Follow the curve from left to right. If the curve goes upward, the function is increasing. If it goes downward, it's decreasing.

What does the interval notation mean?

The notation $-0.45 < x < 0.45$ means we're only looking at x-values between -0.45 and 0.45, not including the endpoints themselves.

Why are there green and blue lines on the graph?

The green line at x = -0.45 and blue line at x = 0.45 mark the boundaries of the interval we need to analyze. They help you focus on the right section of the curve.

What if the function both increases and decreases in the interval?

Look for the overall trend in the given interval. If there are multiple behaviors, the question usually asks for where it's primarily increasing or decreasing.

How can I be sure I'm reading the graph correctly?

Start at the left boundary (x = -0.45) and slowly move your finger to the right boundary (x = 0.45). Watch if your finger moves up (increasing) or down (decreasing).

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