Finding Range of Quadratic Functions

In this video, Avenel Kumar explains how to find the domain and range of a rational function, specifically y = (2x - 3) / x^2. The video highlights the importance of finding both domain and range, unlike most tutorials that focus only on domain. The domain is determined by identifying values that make the denominator zero, while the range is found using a quadratic equation approach. The video concludes with a correction on the range calculation, emphasizing the inclusion of the boundary value.

What is the main focus of this video tutorial?

• Finding both domain and range of a rational function

• Finding the range of a rational function

• Finding the domain of a rational function

• Solving quadratic equations

Why is x not allowed to be zero in the domain of the function y = (2x - 3) / x²?

• Because it makes the function undefined

• Because it makes the denominator zero

• Because it makes the function negative

• Because it makes the numerator zero

What is the domain of the function y = (2x - 3) / x²?

• All negative real numbers

• All positive real numbers

• All real numbers except x = 0

• All real numbers

What method is introduced to find the range of the rational function?

• Quadratic equation method

• Graphical method

• Algebraic method

• Numerical method

What equation is formed to find the range of the function y = (2x - 3) / x²?

• y x² + 2x - 3 = 0

• y x² - 2x + 3 = 0

• y = x² - 2x + 3

• y = 2x - 3

What condition must be satisfied for the quadratic equation to have real solutions?

• b² - 4ac < 0

• b² - 4ac = 0

• b² - 4ac > 0

• b² - 4ac ≤ 0

What is the value of 'b' in the quadratic equation formed for the range?

• 2

• -2

• -3

• 3

What is the value of 'c' in the quadratic equation formed for the range?

• 4

• 3

• 2

• 1

What inequality is solved to find the range of the function?

• 4 - 12y < 0

• 4 + 12y > 0

• 4 + 12y < 0

• 4 - 12y > 0

What is the range of the function y = (2x - 3) / x²?

• y < 1/3

• y ≥ 1/3

• y ≤ 1/3

• y > 1/3