Linear Function Analysis: Finding Positive Values from Graph

Graph Interpretation with Sign Analysis

Look at the linear function represented in the diagram.

When is the function positive?

–8–8–8–7–7–7–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333000

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine when the function is positive?
00:04 The function is positive when it's above the X-axis
00:12 and negative when the function is below the X-axis
00:19 Let's find the point where the function crosses the X-axis
00:23 Here the axis is positive
00:28 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

Look at the linear function represented in the diagram.

When is the function positive?

–8–8–8–7–7–7–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333000

2

Step-by-step solution

The function is positive when it is above the X-axis.

Let's note that the intersection point of the graph with the X-axis is:

(2,0) (2,0) meaning any number greater than 2:

x>2 x > 2

3

Final Answer

x>2 x>2

Key Points to Remember

Essential concepts to master this topic
  • Rule: Function is positive when graph lies above the x-axis
  • Technique: Find x-intercept first: line crosses at (2,0)
  • Check: Test a point like x = 3: function value is positive ✓

Common Mistakes

Avoid these frequent errors
  • Confusing x-values with y-values when reading the graph
    Don't look at y-coordinates to answer when the function is positive = wrong variable! This confuses the input (x) with the output (y). Always remember: 'when is the function positive' asks for x-values where y > 0.

Practice Quiz

Test your knowledge with interactive questions

Look at the function shown in the figure.

When is the function positive?

xy-4-7

FAQ

Everything you need to know about this question

How do I know which part of the line is above the x-axis?

+

Look at the x-intercept where the line crosses the x-axis. In this graph, it's at (2,0) (2,0) . The line goes up as you move right, so for x>2 x > 2 the function is positive.

What does it mean for a function to be positive?

+

A function is positive when its output values (y-values) are greater than zero. On a graph, this means the line or curve is above the x-axis.

Why is the answer x > 2 and not y > 2?

+

The question asks when the function is positive, which means for which x-values. The y-values being positive is the condition, but x-values are what we're looking for as the answer.

How can I double-check my answer?

+

Pick any x-value greater than 2 (like x = 3 or x = 5) and see if the corresponding point on the line is above the x-axis. If yes, your answer is correct!

What if the line was going down instead of up?

+

If the line had a negative slope (going down from left to right), then the function would be positive for x-values less than the x-intercept instead of greater than.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Linear Functions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations