MATHS - Graphs - Asymptotes

The video tutorial explains the concept of asymptotes, which are lines that a curve approaches but never touches. It uses examples like halving and the tangent graph to illustrate how asymptotes occur when a function has no real answer or is undefined. The tutorial covers horizontal, vertical, and oblique asymptotes, emphasizing that they arise when a function approaches a value or when division by zero occurs.

What is an asymptote in mathematical terms?

• A line that a curve crosses at least once

• A curve that crosses a line at multiple points

• A point where two lines intersect

• A line that a curve approaches but never touches

In the context of the tangent function, what happens at 90 degrees?

• The function equals zero

• The function is defined

• The function is undefined

• The function equals one

Which of the following is NOT a type of asymptote?

• Horizontal

• Vertical

• Circular

• Oblique

What condition leads to a vertical asymptote in a function?

• The function is quadratic

• The denominator equals zero

• The function is linear

• The numerator equals zero

What happens when a function's denominator is zero?

• The function equals zero

• The function has a vertical asymptote

• The function has a horizontal asymptote

• The function is defined