Domain and Asymptotes of Functions

In this video, Kumar explains how to find the domain and range of rational functions. The domain is determined by identifying values that make the denominator zero, while the range involves understanding horizontal asymptotes. The video also covers graphing techniques for rational functions, including reciprocal functions, and highlights the importance of symmetry and intercepts in graph analysis.

What is the primary focus of this video tutorial?

• Learning about polynomial functions

• Understanding linear equations

• Exploring quadratic functions

• Finding domain and range of rational functions

What is the first step in finding the domain of a rational function?

• Calculating the y-intercepts

• Identifying the numerator

• Finding the x-intercepts

• Identifying restrictions that make the denominator zero

For the function with a denominator of x + 2, what value of x is excluded from the domain?

• x = 1

• x = 2

• x = -2

• x = 0

What is the domain of a rational function with a denominator of x² + 1?

• x ≠ 0

• All real numbers

• x < 0

• x > 0

What is the domain of the function 1 / (x + 2)?

• x ≠ -2

• x > 0

• x = 0

• x < 0

What is the domain of the function 1 / (x² + 1)?

• x ≠ 0

• All real numbers

• x > 0

• x < 0

What is the domain of the function 2x - 3 / 3x + 6?

• x ≠ -2

• x < 0

• x = 0

• x > 0

What is the domain of the function 1 / (x + 2)?

• x > 0

• x ≠ -2

• x = 0

• x < 0

What is a horizontal asymptote in the context of rational functions?

• A line that the graph never touches

• A point where the graph crosses the x-axis

• A line that the graph approaches as x approaches infinity

• A point where the graph crosses the y-axis

What is the significance of a vertical asymptote in a rational function?

• It indicates where the function is undefined

• It shows where the function has a maximum value

• It represents the x-intercept

• It is the same as the horizontal asymptote