Find Values Where f(x) < 0: Graph Analysis Problem

Q: How do I tell if a function is negative from a graph?

Look for any parts of the curve that are below the x-axis. If the entire graph stays on or above the x-axis (like in this problem), then f(x) ≥ 0 for all values, meaning there are no negative values.

Q: What if the graph touches the x-axis?

When the graph touches the x-axis, f(x) = 0 at that point. This is neither positive nor negative - it's exactly zero. Only look for parts that go below the axis for negative values.

Q: Can a function have no negative values?

Absolutely! Many functions are always positive or zero. For example, $ f(x) = x^2 $ is never negative because squaring any real number gives a non-negative result.

Q: What does 'No such values' mean as an answer?

This means the function never goes below zero anywhere on its domain. The graph either stays above the x-axis or just touches it, but never dips below it.

Q: How is this different from finding where f(x) = 0?

Finding where f(x) = 0 means looking for x-intercepts (where the graph crosses the axis). Finding where f(x) means looking for intervals where the entire curve is below the x-axis.

Graph Analysis with Negative Function Values

Look at the graph below and find all values of $x$ where $f\left(x\right) < 0$ .

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the graph below and find all values of $x$ where $f\left(x\right) < 0$ .

Step-by-step solution

To determine the values of $x$ where $f(x) < 0$ , we need to visually inspect the provided graph to identify any segments where the curve is below the x-axis.

Upon examining the graph:

The function appears to start at a point on the x-axis and follows an upward trajectory, indicating that $f(x) \geq 0$ from this starting point onward.
There are no observed segments where the function dips below the x-axis within the provided graph window, suggesting that $f(x)$ is always non-negative on the domain viewable in the graph.

The conclusion is that there are no values of $x$ for which the function is negative; it remains zero or positive throughout the graph.

Accordingly, the correct answer from the provided choices is choice 3: No such values.

Final Answer

No such values.

Key Points to Remember

Essential concepts to master this topic

Rule: Function is negative when graph lies below x-axis
Technique: Look for portions where curve dips below y = 0
Check: Verify by identifying y-coordinates less than zero ✓

Common Mistakes

Avoid these frequent errors

Confusing x-intercepts with negative regions
Don't assume that points where f(x) = 0 mean f(x) < 0 = wrong identification of negative regions! X-intercepts are where the function crosses the axis, not where it's negative. Always look for sections where the entire curve is below the x-axis.

Practice Quiz

Test your knowledge with interactive questions

The graph of the function below intersects the X-axis at points A and B.

The vertex of the parabola is marked at point C.

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

FAQ

Everything you need to know about this question

How do I tell if a function is negative from a graph?

Look for any parts of the curve that are below the x-axis. If the entire graph stays on or above the x-axis (like in this problem), then f(x) ≥ 0 for all values, meaning there are no negative values.

What if the graph touches the x-axis?

When the graph touches the x-axis, f(x) = 0 at that point. This is neither positive nor negative - it's exactly zero. Only look for parts that go below the axis for negative values.

Can a function have no negative values?

Absolutely! Many functions are always positive or zero. For example, $f(x) = x^2$ is never negative because squaring any real number gives a non-negative result.

What does 'No such values' mean as an answer?

This means the function never goes below zero anywhere on its domain. The graph either stays above the x-axis or just touches it, but never dips below it.

How is this different from finding where f(x) = 0?

Finding where f(x) = 0 means looking for x-intercepts (where the graph crosses the axis). Finding where f(x) < 0 means looking for intervals where the entire curve is below the x-axis.

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