Podcast
Questions and Answers
What are the critical points in a polynomial inequality graph?
What are the critical points in a polynomial inequality graph?
- Points where the graph may change from being above the x-axis to below the x-axis (correct)
- Points where the graph intersects the y-axis
- Points where the graph intersects the x-axis
- Points where the graph is undefined
Which of the following is true about polynomial inequalities with one variable?
Which of the following is true about polynomial inequalities with one variable?
- They have no critical points
- They can only be solved graphically
- They can be solved using sign charts (correct)
- They have an infinite number of solutions
How can graphs be helpful in solving polynomial inequalities?
How can graphs be helpful in solving polynomial inequalities?
- They always give the exact solutions
- They determine the number of solutions
- They provide a visualization to the solutions (correct)
- They show the critical points
What does it mean when (f(x) > 0) in a polynomial inequality?
What does it mean when (f(x) > 0) in a polynomial inequality?
What does it mean when (f(x) < 0) in a polynomial inequality?
What does it mean when (f(x) < 0) in a polynomial inequality?
Sign charts are used to solve polynomial inequalities with ______ variable.
Sign charts are used to solve polynomial inequalities with ______ variable.
The ______ in a polynomial inequality graph are the only places where the graph may possibly change from being above the x-axis to below the x-axis.
The ______ in a polynomial inequality graph are the only places where the graph may possibly change from being above the x-axis to below the x-axis.
In a polynomial inequality, when (f(x) > 0), it means that the function is ______ the x-axis.
In a polynomial inequality, when (f(x) > 0), it means that the function is ______ the x-axis.
Graphs are helpful in providing a visualization to the solutions of ______ inequalities.
Graphs are helpful in providing a visualization to the solutions of ______ inequalities.
In a polynomial inequality, when (f(x) < 0), it means that the function is ______ the x-axis.
In a polynomial inequality, when (f(x) < 0), it means that the function is ______ the x-axis.
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Study Notes
Solving Polynomial Inequalities
- A polynomial inequality is a mathematical statement that relates a polynomial expression as less than or greater than another.
- Sign charts can be used to solve polynomial inequalities with one variable.
- Graphs are helpful in providing a visualization to the solutions of polynomial inequalities.
Critical Points and Intervals
- Critical points are the x-intercepts of a polynomial graph, where the graph may possibly change from being above the x-axis to below the x-axis.
- In a graph, critical points are the only places where the function may change sign (from f(x) > 0 to f(x) < 0).
- Within each interval between two adjacent critical points, the function maintains the same sign (either f(x) > 0 or f(x) < 0).
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