Find Where f(x) < 0: Analyzing Function Values Between x = 1 and x = 7

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

XXXYYY111777444

❤️ Continue Your Math Journey!

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

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

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

XXXYYY111777444

2

Step-by-step solution

To solve the problem of determining where f(x)<0 f(x) < 0 :

  • Step 1: Identify the x-intercepts of the graph, which are x=1 x = 1 and x=7 x = 7 .
  • Step 2: Examine the section of the graph between these intercepts. Since the graph dips below the x-axis between these values, f(x)<0 f(x) < 0 in that interval.

Therefore, the function is negative between the roots, i.e., 1<x<7 1 < x < 7 .

Thus, the solution to the problem is: 1<x<7 1 < x < 7 .

3

Final Answer

1<x<7 1 < x < 7

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 \( f\left(x\right) > 0 \).

AAABBBCCCX

🌟 Unlock Your Math Potential

Get unlimited access to all 18 The Quadratic Function 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

Positive and Negative Domains

Analyzing Function Graphs: Determine Positive X Intervals for f(x)
Click to solve
Solve the Inequality: Find X Where f(x) < 0
Click to solve