Solving One-Variable Inequalities

This video tutorial covers solving inequalities in one variable, focusing on polynomial, rational, and other types of inequalities. It explains how to determine the sign of polynomial functions using graphs and number lines, and how to handle rational inequalities by identifying zeros and vertical asymptotes. The tutorial also addresses square root and absolute value inequalities, emphasizing the importance of domain restrictions and graphing techniques.

What is the primary focus of this section?

• Factoring polynomials

• Graphing linear equations

• Solving inequalities in one variable

• Solving equations in two variables

Which of the following is NOT a learning target mentioned?

• Solving polynomial inequalities

• Finding values causing a rational function to be undefined

• Solving linear equations

• Solving applications involving polynomials and rational inequalities

What is the significance of finding zeros in polynomial inequalities?

• They determine where the polynomial changes sign

• They indicate the maximum value of the polynomial

• They show where the polynomial is undefined

• They are not important in solving inequalities

What happens to the sign of a polynomial at its real zeros?

• It remains the same

• It changes from positive to negative or vice versa

• It becomes undefined

• It always becomes positive

When solving polynomial inequalities, why is it important to consider the intervals between zeros?

• To identify the domain of the polynomial

• To determine the exact value of the polynomial

• To understand the behavior of the polynomial in those intervals

• To find the maximum and minimum points

What is the first step in solving a polynomial inequality?

• Graphing the polynomial

• Factoring the polynomial

• Finding the derivative

• Simplifying the polynomial

How do you determine where a polynomial is positive or negative?

• By finding the derivative

• By graphing the polynomial

• By solving for x

• By testing values in each interval between zeros

What is a vertical asymptote in the context of rational inequalities?

• A point where the function is zero

• A point where the function is undefined

• A point where the function changes sign

• A point where the function has a maximum value

In rational inequalities, what must be considered in addition to zeros?

• Minimum points

• Vertical asymptotes

• Horizontal asymptotes

• Maximum points

How do you solve a rational inequality?

• By making it a single fraction and solving

• By finding the derivative

• By simplifying the numerator

• By graphing the function