Understanding Asymptotes and Function Behavior

The video tutorial covers the concepts of asymptotes, intercepts, and graph behavior. It explains horizontal and vertical asymptotes, how to find x and y intercepts, and the behavior of graphs, particularly hyperbolas. The tutorial also explores approaching asymptotes from different directions and introduces the concept of sine and solving inequalities using graphs.

What is the horizontal asymptote of the function as x approaches infinity?

• y = 0

• y = 1

• x = 1

• x = 0

Which equation represents a vertical asymptote?

• x = 0

• y = 0

• x = 2

• y = 2

How do you find the x-intercept of a function?

• Set x to 0

• Set y to 0

• Set x to 1

• Set y to 1

When x approaches positive infinity, from which direction does the function approach the horizontal asymptote?

• From the left

• From below

• From the right

• From above

What happens to the function as x approaches negative infinity?

• It approaches the horizontal asymptote from above

• It approaches the horizontal asymptote from below

• It remains constant

• It diverges to infinity

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

• It indicates where the function is undefined

• It shows where the function is zero

• It marks the maximum value of the function

• It represents the average value of the function

How can you determine the behavior of a function at large values of x?

• By calculating the derivative

• By analyzing the asymptotes

• By finding the intercepts

• By solving the function's equation

What does the term 'sine' refer to in the context of this lesson?

• The positive or negative nature of a function

• The angle of a triangle

• The area under a curve

• The slope of a line

How can graphs be used to solve inequalities?

• By calculating the area

• By analyzing the sign of the function

• By identifying intercepts

• By finding the slope

What does it mean for a function to be positive in terms of its graph?

• It is below the x-axis

• It is to the right of the y-axis

• It is above the x-axis

• It is to the left of the y-axis