Finding X-Values Where f(x) > 0: Graph Analysis Solution

Graph Analysis with Function Positivity

Based on the data in the sketch, find for which X values the graph of the function f(x)>0 f\left(x\right) > 0

XXXYYY000-2-2-2

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Based on the data in the sketch, find for which X values the graph of the function f(x)>0 f\left(x\right) > 0

XXXYYY000-2-2-2

2

Step-by-step solution

Based on the graph provided, we can see the entire function lies below the x-axis. Thus, there is no interval where f(x)>0 f(x) > 0 .

To solve this problem, here's what we observed:

  • Visual inspection of the graph reveals that it never crosses the x-axis from below.
  • Consequently, the function remains non-positive for all x-values visible, indicating it's non-positive overall within the range observable.

Therefore, the function has no domain where it is positive. Therefore, the solution is:

The function has no domain where it is positive

3

Final Answer

The function has no domain where it is positive

Key Points to Remember

Essential concepts to master this topic
  • Visual Rule: Function is positive where graph lies above x-axis
  • Technique: Check if any part of curve is above y = 0 line
  • Check: Verify entire visible graph stays below or on x-axis ✓

Common Mistakes

Avoid these frequent errors
  • Confusing x-intercepts with positive regions
    Don't think touching the x-axis means the function is positive = zero is not greater than zero! X-intercepts show where f(x) = 0, not where f(x) > 0. Always look for regions where the graph is strictly above the x-axis.

Practice Quiz

Test your knowledge with interactive questions

The graph of the function below does not intersect the \( x \)-axis.

The parabola's vertex is marked A.

Find all values of \( x \) where
\( f\left(x\right) > 0 \).

AAAX

FAQ

Everything you need to know about this question

What does it mean for a function to be positive?

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

Can a function have no positive values?

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Yes! Some functions are always negative or zero. In this case, the entire graph stays below or on the x-axis, so there's no domain where f(x)>0 f(x) > 0 .

What if the graph touches the x-axis?

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If the graph only touches the x-axis, that point has f(x)=0 f(x) = 0 , which is not positive. We need the graph to be strictly above the x-axis for positive values.

How do I read this type of graph question?

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Look at the entire visible portion of the graph. Check if any part rises above the horizontal x-axis line. If not, then there are no positive values.

What's the difference between f(x) > 0 and f(x) ≥ 0?

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f(x)>0 f(x) > 0 means strictly positive (above x-axis only). f(x)0 f(x) ≥ 0 includes zero, so points on the x-axis would also count.

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