Graph Transformations of Rational Functions

The video tutorial explains how to graph the function g(x) = 1/(x-2) + 3 by translating the basic rational function f(x) = 1/x. It demonstrates how the values of C and D affect the graph's translation, with C shifting the graph horizontally and D shifting it vertically. The tutorial provides a step-by-step guide on how to apply these translations to graph g(x) effectively, without the need for a table of values.

What is the basic rational function discussed in the video?

• f(x) = x + 1

• f(x) = 1/x

• f(x) = x^2

• f(x) = x - 1

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

• Shifts the graph right

• Shifts the graph left

• Shifts the graph down

• Shifts the graph up

What happens to the graph of g(x) when C is negative?

• The graph shifts left

• The graph shifts down

• The graph shifts right

• The graph shifts up

If D is positive, how is the graph of g(x) affected?

• The graph shifts left

• The graph shifts down

• The graph shifts right

• The graph shifts up

What is the effect on the graph of g(x) when D is negative?

• The graph shifts right

• The graph shifts down

• The graph shifts left

• The graph shifts up

For g(x) = 1/(x-2) + 3, what is the value of C?

• 2

• -2

• 3

• -3

For g(x) = 1/(x-2) + 3, what is the value of D?

• 2

• -3

• -2

• 3

How many units is the graph of g(x) shifted to the right?

• 1 unit

• 2 units

• 3 units

• 4 units

How many units is the graph of g(x) shifted up?

• 1 unit

• 2 units

• 3 units

• 4 units

What happens to the vertical asymptote when the graph is shifted right?

• It stays the same

• It moves up

• It moves right

• It moves left