Rational Functions Anatomy
Interact with the app below by dragging the TWO LARGE POINTS. Then answer the questions that follow.
What does the [b][color=#38761d]vertical dashed line[/color][/b] represent? Why do you think it exists?
What does the [b][color=#a64d79]horizontal dashed line [/color][/b]represent? Why do you think it exists?
Write the equation of any rational function that never crosses the line [math]x=3[/math].
Write the equation of any rational function that never crosses the lines [math]x=-5[/math] and [math]y=3[/math].
Suppose you graph the [b]rational function [/b][math]y=a\cdot\frac{1}{x}[/math]. [br][br]What does the parameter [math]a[/math] do to the parent graph [math]y=\frac{1}{x}[/math]? How does it affect it? Explain.
Suppose you graph the [b]rational function [/b][math]y=\frac{1}{x-h}[/math]. [br][br]What does the parameter [math]h[/math] do to the parent graph [math]y=\frac{1}{x}[/math]? How does it affect it? Explain.
Suppose you graph the [b]rational function [/b][math]y=\frac{1}{x}+k[/math]. [br][br]What does the parameter [math]k[/math] do to the parent graph [math]y=\frac{1}{x}[/math]? How does it affect it? Explain.