Analyze the Linear Function y = -x - 2: Increasing or Decreasing?

Linear Functions with Negative Slope

Given the following function:

y=x2 y=-x-2

Is the function increasing or decreasing?

–4–4–4–2–2–2222444666–4–4–4–2–2–2222000

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Is the function increasing or decreasing?
00:03 The function equation according to the given data
00:08 Minus is exactly like multiplying by (-1)
00:12 The function's slope is negative according to the given data
00:15 When the function's slope is negative, the function is decreasing
00:19 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

Given the following function:

y=x2 y=-x-2

Is the function increasing or decreasing?

–4–4–4–2–2–2222444666–4–4–4–2–2–2222000

2

Step-by-step solution

To determine if the function y=x2 y = -x - 2 is increasing or decreasing, we analyze its slope.

  • Step 1: Identify the slope. The given function is in the form y=mx+b y = mx + b , where m m is the slope. Here, m=1 m = -1 .
  • Step 2: Analyze the slope. Since m=1 m = -1 , which is less than 0, the slope is negative.
  • Step 3: Conclude based on the slope. For a linear function, if the slope is negative (m<0 m < 0 ), the function is said to be decreasing.

Therefore, the function is Decreasing.

3

Final Answer

Decreasing

Key Points to Remember

Essential concepts to master this topic
  • Slope Rule: Negative slope means function decreases as x increases
  • Technique: In y=x2 y = -x - 2 , slope m = -1 < 0
  • Check: Pick two x-values: when x increases, y decreases ✓

Common Mistakes

Avoid these frequent errors
  • Confusing slope sign with y-intercept sign
    Don't look at the -2 to determine if the function increases or decreases! The y-intercept doesn't affect whether a function increases or decreases. Always focus on the coefficient of x (the slope) to determine if the function is increasing or decreasing.

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 linear function is increasing or decreasing just by looking at it?

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Look at the coefficient of x (the slope). If it's positive, the function is increasing. If it's negative, the function is decreasing. In y=x2 y = -x - 2 , the coefficient of x is -1, so it's decreasing.

What does it mean for a function to be decreasing?

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A decreasing function means that as x-values get larger, the y-values get smaller. Think of it like going downhill - as you move right on the graph, the line goes down.

Does the y-intercept affect whether a function increases or decreases?

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No! The y-intercept (-2 in this case) only tells you where the line crosses the y-axis. It doesn't change the direction of the line. Only the slope determines if the function increases or decreases.

How can I verify my answer using the graph?

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Look at the line from left to right. If it's going downward, the function is decreasing. If it's going upward, the function is increasing. You can also pick any two points and check if y decreases as x increases.

What if the slope is zero?

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If the slope is zero (like y=5 y = 5 ), the function is neither increasing nor decreasing - it's constant! The line is horizontal.

Can I use specific points to check if a function is decreasing?

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Yes! Pick any two points. For y=x2 y = -x - 2 : when x = 0, y = -2; when x = 1, y = -3. Since y went from -2 to -3 (decreased) while x increased, the function is decreasing.

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