Understanding Rational Inequalities and Graphs

The video tutorial explains how to solve rational inequalities by factoring the numerator and denominator, finding their zeros, plotting these zeros on a number line, and testing intervals to determine which satisfy the inequality. It also covers how to represent solutions graphically and verify them using interval notation and inequalities.

What is the first step in solving a rational inequality?

• Testing intervals

• Factoring the numerator and denominator

• Finding the solution graphically

• Plotting the zeros on a number line

When factoring the numerator, which expression represents a difference of squares?

• X^2 - 9

• X + 3 and X - 3

• X^2 + 5X - 6

• X + 6 and X - 1

What type of points are used for zeros of the denominator on a number line?

• Dashed points

• Solid points

• Open points

• Closed points

Which test value is used to check the interval between -6 and -3?

• X = -7

• X = 2

• X = -5

• X = 0

What is the result of testing X = 0 in the inequality?

• The result is undefined

• The interval is not part of the solution

• The result is negative

• The interval is part of the solution

How is the solution expressed using interval notation?

• From negative infinity to positive infinity

• From -3 to 3, including both

• From -6 to 1, excluding 1

• From negative infinity to -6, union -3 to 1, union 3 to infinity

What does the graphical method help determine?

• When the graph is undefined

• When the graph intersects the Y-axis

• When the graph is on or above the X-axis

• When the graph is below the X-axis

Which interval is confirmed by the graph to satisfy the inequality?

• X < 3

• X = 0

• X > 1

• X < -6

What is the significance of the vertical asymptote at X = 1?

• It changes the inequality direction

• It makes the graph undefined

• It excludes X = 1 from the solution

• It includes X = 1 in the solution

Why is it important to understand both graphical and algebraic methods?

• To simplify the inequality

• To avoid using a calculator

• To verify solutions and understand the problem comprehensively

• To solve inequalities faster