First and last name:
Open book (but don't use the method from the book), calculators allowed.
1. [10 points ] Draw the graph of
( )=
r x
x
x
2
, 16
using the 6-step procedure introduced in lectures. Most of the points are for
your working and PRESENTATION, so explain what you're doing in each
step.
Solution:
1. Not the translate of a simple function.
2. Find -intercepts (1 point): = (0) = 0 (1 point).
3. (a) Find -intercepts (1 point): solve ( ) = 0 so = 0 (1 point).
(b) Find vertical asymptotes (1 point): solve 2 , 16 = 0 so = 4 (1
point).
4. Find far left / far right behaviour:
y
y
r
x
r x
x
x
1 = degree
f <
x
degree = 2
g
;
(1 point) so = 0 is a horizontal asymptote (1 point).
5. Plot one point between and beyond the zeroes and vert. asymptotes at =
,4 0 4. Thus, for example, calculate (,5) = ,5 9, (,2) = 1 6, (2) =
,1 6, (5) = 5 9 (1 point).
6. Now just draw the graph (1 point) as follows. From = 0 at far left it
drops through (,5 ,5 9) down towards ,1 at the vert asymptote = ,4.
On right hand side of = ,4 it drops from +1 through (,2 1 6), then
through the origin, then through (2 ,1 6) and down towards ,1 at the
vert asymptote = 4. On right hand side of = 4 it drops from +1
through (5 1 5 9), then on towards = 0 at the far right.
y
x
;
=
;
r
r
=
r
=
r
=
y
;
=
x
x
;
;
x
;
=
x
= =
y
1
=