Identify the Declining Interval: Locate the Function's Decrease Near x = 1.3

Function Behavior with Decreasing Intervals

In which interval does the function decrease?

Red line: x=1.3 x=1.3

–4–4–4–2–2–2222444666888101010–2–2–2222444000

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the decreasing domain of the function
00:04 The function decreases when X values increase and Y values decrease
00:10 Let's start by finding the increasing domains
00:19 Between the increasing domains, the function decreases
00:25 This is the decreasing domain
00:31 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

In which interval does the function decrease?

Red line: x=1.3 x=1.3

–4–4–4–2–2–2222444666888101010–2–2–2222444000

2

Step-by-step solution

To solve this problem, we need to determine the interval on which the function is decreasing. We have visual aid from a graph and a red line denoting x=1.3 x = 1.3 . Upon inspecting the graph:

  • The function appears to decrease between two points. This interval is crucial to identify, particularly in relation to the line x=1.3 x = 1.3 .
  • To determine the decreasing interval, note where the graph slopes downward. Upon doing so, the graph descends in the range between x=−1.3 x = -1.3 and x=1.3 x = 1.3 .

Therefore, the function decreases in the interval −1.3<x<1.3 -1.3 < x < 1.3 .

Given the choices, the correct choice is 1.3>x>−1.3 1.3 > x > -1.3 .

3

Final Answer

1.3>x>−1.3 1.3 > x > -1.3

Key Points to Remember

Essential concepts to master this topic
  • Definition: Function decreases when graph slopes downward from left to right
  • Reading Graphs: Look between x=−1.3 x = -1.3 and x=1.3 x = 1.3 for downward slope
  • Verification: Check that y-values get smaller as x-values increase ✓

Common Mistakes

Avoid these frequent errors
  • Confusing interval notation order
    Don't write 1.3<x<−1.3 1.3 < x < -1.3 = impossible interval! This means x is both greater than 1.3 AND less than -1.3, which is mathematically impossible. Always write intervals with smaller value first: −1.3<x<1.3 -1.3 < x < 1.3 or equivalently 1.3>x>−1.3 1.3 > x > -1.3 .

Practice Quiz

Test your knowledge with interactive questions

Does the function in the graph decrease throughout?

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FAQ

Everything you need to know about this question

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

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Look at the graph from left to right. If the curve is going downward (like walking downhill), then the function is decreasing in that interval. The y-values get smaller as x-values get larger.

What's the difference between −1.3<x<1.3 -1.3 < x < 1.3 and 1.3>x>−1.3 1.3 > x > -1.3 ?

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They mean exactly the same thing! Both say that x is between -1.3 and 1.3. The first reads "x is greater than -1.3 and less than 1.3" while the second reads "1.3 is greater than x and x is greater than -1.3."

Why does the red line at x = 1.3 matter?

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The red line at x=1.3 x = 1.3 helps you locate the boundary of the decreasing interval. It shows where the function stops decreasing and the interval ends.

Can a function decrease in multiple intervals?

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Absolutely! Many functions have several intervals where they decrease. For this problem, we're focusing on the interval near x = 1.3 as mentioned in the question.

What if I can't see the graph clearly?

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Look for these clues:

  • Downward slope - the curve goes down from left to right
  • Negative rate of change - y decreases as x increases
  • Peak and valley pattern - function decreases between a high point and low point

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