Peer Instruction for September 8 and 9.




Exercise 1. If $f(x)$ = MATH and MATH

(a) find the horizontal and vertical aysmptotes of $f$;

(b) graph function $y=f(x)$,

(c) graph $y=g(x),$

(d) solve $f(x)>0$ or $f(x)<0$,

(e) solve $g(x)>0$ or $g(x)<0.$

Exercise 2. If $f(x)=$ MATH and MATH

(a) find the horizontal and vertical aysmptotes of $f$;

(b) graph $y=f(x),$,

(c) graph $y=g(x),$

(c) solve $f(x)>0$ or $f(x)<0$. [Note that MATH and solving $f(x)>0$ is the same as sovling MATH.

Exercise 3. If MATH and $g(x)=2(x-1)(x-2).$

(a) find the horizontal and vertical aysmptotes of f,

(b) graph $y=f(x)$,

(c) graph $y=g(x),$

(d) solve $f(x)>0$ or $f(x)<0$,

(e) solve $g(x)>0$ or $g(x)<0.$[[*Note that solving $f(x)>0$ is the same as solving $g(x)>0$.]

Exercise 4: Find two rational functions $f$ which satisfy all the following conditions and use a technology to check your answers.

(1) the vertical asymptotes of $f$ are at $x=1$ and $x=-3$,

(2) the horizontal asymptote of $f$ is at $y=2$,

(3) $f(0)=3$.

[hint: try MATH and MATH