Understanding Function Behavior and Asymptotes

The video tutorial explains how to find the domain and range of the function f(x) = 2x/(x^2 - 16). It begins by identifying the domain, which includes all x-values except those that make the denominator zero, specifically x = ±4. The range is determined by analyzing the graph of the function, noting that it approaches vertical asymptotes at x = ±4 and extends to all real numbers. The tutorial emphasizes understanding these concepts through set notation and graphical representation.

What is the function f(x) discussed in the video?

• f(x) = 2x / (x^2 - 16)

• f(x) = x^2 / (2x - 16)

• f(x) = 2x^2 / (x - 16)

• f(x) = 2 / (x^2 - 16)

What condition makes a function undefined?

• When the denominator is zero

• When the numerator is zero

• When x is negative

• When x is positive

What equation do we solve to find when the function is undefined?

• x^2 + 16 = 0

• x^2 - 16 = 0

• 2x - 16 = 0

• 2x + 16 = 0

What are the values of x that make the function undefined?

• x = ±16

• x = ±4

• x = 16

• x = 0

How is the domain of the function expressed in set notation?

• All x such that x = ±4

• All x such that x ≠ ±4

• All x such that x > 4

• All x such that x < 4

What is the range of a function?

• All possible y values

• All possible x values

• All negative y values

• All positive x values

What tool can help visualize the range of a function?

• A protractor

• A calculator

• A graph

• A ruler

What are vertical asymptotes?

• Horizontal lines

• Lines the graph approaches but never touches

• Lines the graph crosses

• Diagonal lines

Where are the vertical asymptotes for this function?

• x = 0

• x = ±4

• x = ±16

• x = 16

What happens to the graph near the vertical asymptotes?

• It crosses the asymptotes

• It shoots up or down

• It remains flat

• It curves back