Reciprocal Function Concepts and Transformations

The video tutorial explains how to graph the basic reciprocal function y = 1/x, highlighting the importance of asymptotes at x = 0 and y = 0. It demonstrates how to plot key points and discusses the behavior of the graph near asymptotes. The tutorial also covers transformations of the reciprocal function, showing how changes in the equation affect the graph's position and asymptotes.

What is the basic form of the reciprocal function?

• y = x

• y = x + 1

• y = 1/x

• y = x^2

Why can't the reciprocal function be evaluated at x = 0?

• It results in a zero value.

• It results in a negative value.

• It results in an undefined value.

• It results in a positive value.

What is an asymptote in the context of the reciprocal function?

• A line that the graph approaches but never touches.

• A line that the graph intersects at multiple points.

• A point where the graph crosses the axis.

• A point where the graph reaches its maximum.

What is the y-value when x = 1 in the reciprocal function?

• Undefined

• 2

• 1

• 0

What is the y-value when x = 2 in the reciprocal function?

• 0

• 1

• 2

• 1/2

What happens to the y-value when x = 1/2 in the reciprocal function?

• It becomes 0.

• It becomes 1.

• It becomes 2.

• It becomes 1/2.

What is the y-value when x = 4 in the reciprocal function?

• 0

• 4

• 1/4

• 1

What is the y-value when x = 1/4 in the reciprocal function?

• 0

• 1

• 4

• 1/4

How does the graph of the reciprocal function change with negative x-values?

• It remains in the first quadrant.

• It remains unchanged.

• It mirrors in the third quadrant.

• It mirrors in the second quadrant.

What are the key points to plot for the parent reciprocal function?

• (2, 2) and (-2, -2)

• (1, 1) and (-1, -1)

• (0, 0) and (1, 1)

• (1, 0) and (0, 1)