Understanding Graph Transformations of Rational Functions

The video tutorial explains how to graph the function g(x) = 1/(x+1) - 2 using the basic rational function f(x) = 1/x. It covers how the values of C and D affect the graph's horizontal and vertical shifts, respectively. The tutorial provides an example of these transformations and demonstrates how to apply them to graph g(x) by shifting key points and asymptotes.

What is the basic rational function discussed in the video?

• f(x) = x + 1

• f(x) = x^2

• f(x) = 1/x

• f(x) = x - 1

How does a positive constant C affect the graph of a rational function?

• Shifts the graph downwards

• Shifts the graph to the left

• Shifts the graph upwards

• Shifts the graph to the right

What happens to the graph when the constant C is negative?

• The graph shifts left

• The graph shifts right

• The graph shifts up

• The graph shifts down

If D is positive, how is the graph of the function affected?

• The graph shifts up

• The graph shifts right

• The graph shifts down

• The graph shifts left

What is the effect on the graph when D is negative?

• The graph shifts left

• The graph shifts right

• The graph shifts up

• The graph shifts down

In the example, what is the value of C?

• C = 0

• C = -1

• C = 2

• C = 1

In the example, what is the value of D?

• D = -2

• D = -1

• D = 2

• D = 0

How is the graph shifted when C = 1 and D = -2?

• Right 1 unit, down 2 units

• Left 1 unit, up 2 units

• Right 1 unit, up 2 units

• Left 1 unit, down 2 units

What is the first step in graphing the transformed function?

• Shift key points right and up

• Shift the graph up

• Shift the graph down

• Shift key points left and down

How are the asymptotes affected by the transformations?

• Vertical asymptote shifts down, horizontal shifts left

• Vertical asymptote shifts up, horizontal shifts right

• Vertical asymptote shifts left, horizontal shifts down

• Vertical asymptote shifts right, horizontal shifts up