Solving One-Variable Inequalities

The video tutorial covers solving inequalities in one variable, focusing on polynomial, rational, and radical inequalities. It explains how to determine where a function is positive or negative using number lines and sign charts. The tutorial also demonstrates graphical solutions for polynomial inequalities and discusses the zero product property for solving radical inequalities.

What does the symbol 'greater than or equal to' indicate in the context of polynomial inequalities?

• Where the function is negative

• Where the function is zero

• Where the function is positive

• Where the function is undefined

In the example f(x) = (x + 3)(x - 4)^2, what are the zeros of the polynomial?

• x = -3 and x = 4

• x = 3 and x = -4

• x = 0 and x = 4

• x = -3 and x = -4

When creating a positive-negative chart, what is the purpose of plugging in numbers into the polynomial?

• To find the derivative of the polynomial

• To simplify the polynomial

• To find the exact value of the polynomial

• To determine the intervals where the polynomial is positive or negative

How do you determine the intervals where a polynomial is positive or negative using a graph?

• By finding the slope of the graph

• By calculating the area under the curve

• By finding the maximum and minimum points

• By identifying the zeros and analyzing the sign changes

What are the zeros of the polynomial x^3 - 6x^2 + 8x - 2 when solved graphically?

• 0.32, 1.46, and 4.21

• 0.32, 1.56, and 4.21

• 0.32, 1.46, and 3.21

• 0.42, 1.46, and 4.21

In the rational function r(x) = (x + 3)(x - 5) / (5x - 2), what makes the function undefined?

• x = 0

• x = 2/5

• x = 5

• x = -3

What is the purpose of creating a sign chart for rational functions?

• To determine the intervals where the function is positive or negative

• To find the derivative of the function

• To find the exact value of the function

• To simplify the function

In the inequality involving a radical, why is any value less than -1 considered undefined?

• Because it results in a negative value under the square root

• Because it makes the denominator zero

• Because it makes the numerator zero

• Because it results in a positive value under the square root

What are the zeros of the function in the inequality involving a radical?

• x = -1 and x = 1

• x = 0 and x = 2

• x = 2 and x = -1

• x = 1 and x = -2

When solving inequalities involving radicals, what type of chart is used to determine the intervals?

• A positive-negative chart

• A derivative chart

• A slope chart

• A value chart