Rational Inequalities Quiz

What is the first step in solving a rational inequality?

• Find the common denominator

• Graph the inequality

• Combine all terms into one fraction

• Set the inequality to zero

In the first example, why can't the denominator be zero?

• It would make the fraction zero

• It would make the fraction undefined

• It would make the fraction positive

• It would make the fraction negative

What does a closed circle on the number line indicate?

• The value is excluded from the solution

• The value is included in the solution

• The value is a horizontal asymptote

• The value is a vertical asymptote

What does the graph of a rational inequality help determine?

• Where the graph is above or below the x-axis

• The exact solution of the inequality

• The common denominator

• The factors of the numerator

In the second example, what is the purpose of finding a common denominator?

• To factor the numerator

• To simplify the inequality

• To graph the inequality

• To combine fractions into one

Why are some points on the number line open circles in the second example?

• They are where the numerator is zero

• They are where the denominator is zero

• They are where the inequality is positive

• They are solutions to the inequality

In the third example, what is the significance of factoring the numerator and denominator?

• It identifies the vertical asymptotes

• It simplifies the inequality

• It helps in finding the test points

• It determines the graph's shape

What does a positive result in a test interval indicate?

• The interval is not part of the solution

• The interval is part of the solution

• The interval is a vertical asymptote

• The interval is a horizontal asymptote

In the third example, why is it important to test multiple intervals?

• To graph the inequality

• To factor the numerator

• To ensure all possible solutions are found

• To find the common denominator

What does the solution in interval notation represent?

• The common denominator

• The factors of the numerator

• The exact points where the inequality is zero

• The range of x-values where the inequality holds