Asymptotes and Domains of Functions

The video tutorial covers section 8.2 on reciprocal function families, focusing on graphing these functions. It explains the general form of reciprocal functions and the significance of asymptotes. The tutorial includes examples with H and K values as zero, a negative A value, and non-zero H and K values, demonstrating how to graph these functions and determine their domain and range.

What is the general form of a reciprocal function?

• y = a / (x - h) + k

• y = ax + h + k

• y = a(x - h) + k

• y = a(x + h) - k

In a reciprocal function, what role do H and K play?

• They are the coefficients of x.

• They determine the slope of the graph.

• They are constants that do not affect the graph.

• They determine the position of the asymptotes.

Where does the vertical asymptote occur in a reciprocal function?

• At y = 0

• At x = 0

• At x = h

• At y = k

Where does the horizontal asymptote occur in a reciprocal function?

• At x = 0

• At x = h

• At y = 0

• At y = k

What happens to the asymptotes when H and K are both zero?

• They become undefined.

• They shift to x = h and y = k.

• They remain at x = 0 and y = 0.

• They disappear.

When graphing y = 2/x, which x-values should be avoided?

• x = 0

• x = 1

• x = 2

• x = -1

What is the domain of the function y = 2/x?

• x > 0

• x < 0

• All real numbers except x = 0

• All real numbers

What is the range of the function y = 2/x?

• y > 0

• All real numbers except y = 0

• y < 0

• All real numbers

How does a negative 'a' value affect the graph of a reciprocal function?

• It shifts the graph upwards.

• It reflects the graph across the y-axis.

• It reflects the graph across the x-axis.

• It shifts the graph downwards.

What is the domain of a reciprocal function with a negative 'a' value?

• x < 0

• x > 0

• All real numbers except x = 0

• All real numbers