Evaluate the limit of the reciprocal function with an asymptote

The video tutorial reviews graphing techniques, focusing on reciprocal functions and transformations. It explains how to graph using vertical stretch and horizontal shift, and discusses the concept of asymptotes, particularly vertical asymptotes. The tutorial also covers limits, emphasizing that the left and right hand limits do not converge at a vertical asymptote, leading to a 'does not exist' conclusion.

What transformations are applied to the reciprocal function in the video?

• Vertical stretch by a factor of 3 and horizontal shift 2 units to the left

• Vertical stretch by a factor of 2 and horizontal shift 2 units to the right

• Vertical stretch by a factor of 3 and horizontal shift 1 unit to the left

• Vertical compression by a factor of 3 and horizontal shift 1 unit to the right

Why is direct substitution not applicable in the given scenario?

• Because it results in a division by zero

• Because it results in a complex number

• Because it results in a negative number

• Because it results in an undefined variable

What is the appearance of the graph based on the transformations discussed?

• A straight line

• A parabolic curve

• A hyperbolic curve

• A circular shape

What happens to the limits as the graph approaches the vertical asymptote?

• The left-hand and right-hand limits diverge to different values

• The left-hand and right-hand limits converge to the same value

• The limits become undefined

• The limits approach infinity

Why does the limit not exist at the vertical asymptote?

• Because the function is continuous at that point

• Because the left-hand and right-hand limits do not match

• Because the function is differentiable at that point

• Because the function is undefined at that point