Solving and Graphing Polynomial and Rational Inequalities

The video tutorial covers graphing and solving inequalities, including polynomial and rational inequalities. It begins with a basic introduction to inequalities, explaining the difference between equations and inequalities. The tutorial then demonstrates how to solve polynomial inequalities using number lines and test points. It also covers graphing two-variable inequalities by treating them as equations and shading the solution area. Finally, the video explains rational inequalities, focusing on finding x-intercepts and vertical asymptotes. The tutorial concludes with a comprehension check.

What is the main difference between an equation and an inequality?

• An equation shows a relationship of equality, while an inequality shows a relationship of inequality.

• An equation can only have one variable, while an inequality can have multiple.

• An equation always has a solution, while an inequality does not.

• An equation is always linear, while an inequality is not.

When solving the inequality x^2 + 6x < -5, what is the first step?

• Subtract 6x from both sides.

• Add 5 to both sides.

• Divide both sides by x.

• Multiply both sides by -1.

How do you determine which sections of the number line satisfy a polynomial inequality?

• By solving the inequality for x.

• By testing points in each section of the number line.

• By using the quadratic formula.

• By graphing the inequality.

What does shading above a line in a graph of a two-variable inequality represent?

• All points on and above the line are solutions.

• All points below the line are solutions.

• Only the points on the line are solutions.

• The line itself is the only solution.

In the inequality y > x^2 - 4, what does the graph represent?

• A line shifted up by 4 units.

• A parabola with solutions below it.

• A circle with solutions inside it.

• A parabola with solutions above it.

What is the x-intercept of the rational inequality 2x + 2 over x + 3 > 0?

• 1

• -3

• 0

• -1

How do you find the vertical asymptote of a rational inequality?

• Set the numerator equal to zero.

• Set the denominator equal to zero.

• Graph the function and find where it crosses the x-axis.

• Solve the inequality for x.