Linear Function Analysis: Identifying Decreasing Behavior from a Graph

Linear Functions with Slope Interpretation

Is the function in the graph below decreasing?

yx

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Is the function in the graph below decreasing?

yx

2

Step-by-step solution

To determine if the function is decreasing, we will analyze the graph visually:

The graph shows a line connecting from the bottom-left to the top-right of the graph area, indicating the line has a positive slope. This type of graph indicates the function is increasing, not decreasing.

A decreasing function means its value goes down as x x increases, which is equivalent to having a negative slope.

Since the graph appears with a positive slope, the function is not decreasing.

Thus, the correct choice to the problem, which asks if the function in the graph is decreasing, is No.

3

Final Answer

No

Key Points to Remember

Essential concepts to master this topic
  • Rule: Decreasing functions have negative slopes going down left-to-right
  • Technique: Positive slope means function increases as x increases
  • Check: Trace the line: starts low-left, ends high-right = increasing ✓

Common Mistakes

Avoid these frequent errors
  • Confusing positive and negative slopes
    Don't say a line going up from left to right is decreasing = wrong classification! This confuses slope direction with function behavior. Always remember: upward slope means increasing function, downward slope means decreasing function.

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 can I tell if a function is increasing or decreasing just by looking?

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Look at the direction the line goes from left to right. If it goes upward, the function is increasing. If it goes downward, it's decreasing!

What does slope have to do with increasing or decreasing?

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Positive slope = increasing function (line goes up). Negative slope = decreasing function (line goes down). Zero slope = constant function (horizontal line).

Can a function be both increasing and decreasing?

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A linear function (straight line) is either always increasing, always decreasing, or constant. Only curved functions can increase in some parts and decrease in others.

What if the line is very steep - does that matter?

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The steepness tells you how quickly the function increases or decreases, but doesn't change whether it's increasing or decreasing. A steep upward line is still increasing!

How do I remember which direction means increasing?

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Think of climbing stairs: going up (left to right) means you're increasing your height. Going down means you're decreasing your height!

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