Understanding Function Transformations and Asymptotes

The video tutorial explains how to find the domain, range, horizontal asymptote, and vertical asymptote of the function f(x) = 1/(x-2) + 4. It uses transformations of the basic function g(x) = 1/x, reviewing its properties and graph. The tutorial covers horizontal and vertical shifts, showing how these affect the graph and asymptotes. It concludes by determining the domain and range of f(x), emphasizing the effects of transformations on these properties.

What is the primary goal when analyzing the function f(x) in this video?

• To solve for x when f(x) equals zero

• To find the maximum value of f(x)

• To calculate the derivative of f(x)

• To determine the domain, range, and asymptotes

What is the domain of the basic function g(x) = 1/x?

• All real numbers except x cannot equal zero

• All real numbers

• All negative numbers

• All positive numbers

What is the range of the basic function g(x) = 1/x?

• All positive numbers

• All real numbers except y cannot equal zero

• All negative numbers

• All real numbers

How is the function f(x) derived from g(x) = 1/x?

• By reflecting g(x) over the x-axis

• By shifting g(x) right and up

• By adding 5 to g(x)

• By multiplying g(x) by 2

What happens to the graph of g(x) when it is shifted right by two units?

• The graph moves up by two units

• The graph moves left by two units

• The graph moves down by two units

• The graph moves right by two units

How does a positive value of 'b' affect the graph of g(x)?

• Shifts the graph down

• Shifts the graph up

• Shifts the graph right

• Shifts the graph left

What is the vertical asymptote of the function f(x) after transformation?

• x = 0

• x = 2

• x = -2

• x = 4

What is the horizontal asymptote of the function f(x) after transformation?

• y = 0

• y = 2

• y = 4

• y = -4

What is the domain of the function f(x) after transformation?

• All real numbers

• All real numbers except x cannot equal two

• All positive numbers

• All negative numbers

What is the range of the function f(x) after transformation?

• All real numbers

• All real numbers except y cannot equal four

• All positive numbers

• All negative numbers