Graphing Translations of Rational Functions

This video tutorial explains how to graph translations of the basic rational function f(x) = 1/x. It covers the effects of horizontal and vertical shifts on the graph, determined by the values of 'c' and 'd'. The tutorial includes examples of graphing g(x) = 1/(x+3) and g(x) = 1/(x-2), demonstrating how to apply these translation principles to shift key points and asymptotes. The video concludes with additional examples to reinforce the concepts.

What is the parent rational function discussed in the video?

• f(x) = x^2

• f(x) = 1/x

• f(x) = sqrt(x)

• f(x) = x^3

If 'c' is positive, in which direction does the graph shift?

• Up

• Down

• Left

• Right

What happens to the graph when 'c' is negative?

• It shifts left

• It shifts down

• It shifts right

• It shifts up

How does a positive 'd' value affect the graph?

• Shifts it up

• Shifts it left

• Shifts it right

• Shifts it down

What is the effect of a negative 'd' value on the graph?

• Shifts it right

• Shifts it left

• Shifts it down

• Shifts it up

When graphing g(x) = 1/(x+3), how many units is the graph shifted?

• 1 unit right

• 3 units left

• 3 units right

• 1 unit left

What happens to the vertical asymptote when graphing g(x) = 1/(x+3)?

• It shifts right

• It shifts up

• It shifts down

• It shifts left

In graphing g(x) = 1/(x-2), what type of shift occurs?

• Left shift

• Downward shift

• Right shift

• Upward shift

For g(x) = 1/(x+1), what is the direction of the shift?

• Down

• Up

• Left

• Right

Why is understanding translations important for graphing?

• It only applies to linear functions

• It is not important

• It simplifies graphing complex functions

• It helps in solving equations