Copy of Sketching y = 1/f(x)

Refresher

For the function [math]f\left(x\right)=\frac{1}{x}[/math] [br]as [math]x\longrightarrow0[/math][br][math]f\left(x\right)\longrightarrow\infty[/math][br]

1) The graph of f(x)=x and its reciprocal

2) The graph of f(x)=x+2 and its reciprocal

Using your calculator, observe what happens if we substitute the x-intercept of the function into the reciprocal.[br][br]By analysing the graphs, which of the following is true?

[math]f\left(x\right)\longrightarrow0,g\left(x\right)\longrightarrow\infty[/math] [math]f\left(x\right)\longrightarrow\infty,g\left(x\right)\longrightarrow0[/math] [math]f\left(x\right)\longrightarrow\infty,g\left(x\right)\longrightarrow\infty[/math] [math]f\left(x\right)\longrightarrow0,g\left(x\right)\longrightarrow0[/math]

What feature of the functions corresponds to the vertical asymptotes in the reciprocal graphs?

3) The graph of f(x)=x and its reciprocal

What are the points of intersection between the graphs above?

4) The graph of f(x)=x and its reciprocal