Practice section 2 of 9

State the transformation which transforms $y=1+1/(x+1)$ to $y=1+1/(2x+1)$. On separate diagrams, sketch the two graphs, stating the equations of any asymptotes.

Use a graphing calculator to sketch:

1. $y=(x+1)(x-3)$
2. $y=\frac12(x+1)(x-3)$
3. $y=2(x+1)(x-3)$

Copy the curves. What do you observe about the curves?

State the transformation which transforms $y=1+1/(x+1)$ to $y=2(1+1/(x+1))$. On separate diagrams, sketch the two graphs, stating the equations of any asymptotes.

Given $f(x)=x+1$, sketch on separate diagrams (a) $y=2f(x)$ and (b) $y=f(2x)$.

Use a graphing calculator to sketch (1) $y=(x+1)(x-3)$ and (2) $y=-(x+1)(x-3)$. Copy the curves. What do you observe about the curves?

State the transformation which transforms $y=1+1/(x+1)$ to $y=-1-1/(x+1)$. On separate diagrams, sketch the two graphs, stating the equations of any asymptotes.