Find X Values Where the Function f(x) < 0: Graph Analysis

Q: How do I know which parts of the graph are negative?

Look for where the curve is below the x-axis. When a graph dips below the horizontal line y = 0, those are the negative values of the function.

Q: What do the points x = -2 and x = 2 represent?

These are x-intercepts or zeros of the function - where f(x) = 0. They mark the boundary points where the function changes from positive to negative or vice versa.

Q: Why isn't the answer x 2?

That would be where the function is positive (above the x-axis). Since we want f(x)

Q: Do I include the points -2 and 2 in my answer?

No! At x = -2 and x = 2, the function equals zero $ f(x) = 0 $, not less than zero. Use strict inequality signs: \( -2 .

Q: How can I double-check my answer?

Pick a test point inside your interval, like x = 0. Look at the graph: is f(0) below the x-axis? If yes, your interval is correct!

Graph Analysis with Function Inequality

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

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

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

Step-by-step solution

To solve the problem of finding for which $x$ values the function $f(x) < 0$ , we proceed as follows:

First, we observe the provided graph of the function. Our goal is to identify the intervals on the $x$ -axis where the curve of the function is below the line $y = 0$ (the x-axis). These intervals represent where the function $f(x)$ takes negative values.

Upon examining the graph, we notice that:

The curve descends below the x-axis starting once it crosses $x = -2$ .
It continues below the x-axis until it reaches $x = 2$ .
Therefore, the function is negative between these two points.

Based on the graph, the interval where $f(x) < 0$ is from $x = -2$ to $x = 2$ . Thus, the correct mathematical statement for the values of $x$ where $f(x) < 0$ is $-2 < x < 2$ .

The correct choice from the options given is $-2 < x < 2$ .

Therefore, the solution to the problem is $-2 < x < 2$ .

Final Answer

$-2 < x < 2$

Key Points to Remember

Essential concepts to master this topic

Negative Values: Function is negative when graph is below x-axis
Technique: Find x-intercepts at -2 and 2, function negative between them
Check: Pick test point like x = 0: graph shows f(0) < 0 ✓

Common Mistakes

Avoid these frequent errors

Reading where function is positive instead of negative
Don't look for where the graph is above the x-axis when asked for f(x) < 0! This gives the opposite answer. The graph above x-axis means f(x) > 0, not f(x) < 0. Always identify that 'less than zero' means below 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
$f\left(x\right) > 0$ .

FAQ

Everything you need to know about this question

How do I know which parts of the graph are negative?

Look for where the curve is below the x-axis. When a graph dips below the horizontal line y = 0, those are the negative values of the function.

What do the points x = -2 and x = 2 represent?

These are x-intercepts or zeros of the function - where f(x) = 0. They mark the boundary points where the function changes from positive to negative or vice versa.

Why isn't the answer x < -2 or x > 2?

That would be where the function is positive (above the x-axis). Since we want f(x) < 0, we need the interval where the graph is below the x-axis, which is between the zeros.

Do I include the points -2 and 2 in my answer?

No! At x = -2 and x = 2, the function equals zero $f(x) = 0$ , not less than zero. Use strict inequality signs: $-2 < x < 2$ .

How can I double-check my answer?

Pick a test point inside your interval, like x = 0. Look at the graph: is f(0) below the x-axis? If yes, your interval is correct!

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