Assignment, pencil red pen, highlighter,
GP notebook, graphing calculator
Graph each function on the same set of
axes. Be sure to identify the inflection point.
y
10
f(x) = (x + 4)3 – 2
f(x) = (x + 4)3 – 2
inflection point: (–4, –2)
1
f(x)  x  5 3  3
2
inflection point:
8
6
+1
4
+3
(5, 3)
+1
2
–10 –8 –6 –4 –2
2
–2
–4
total:
–6
8
+3
–8
–10
4
6
f(x) 
8 10
x
1
x  5 3  3
2
PG – 77
Asymptote: A line that is a close approximation to a particular curve
as the curve goes off to infinity in one direction. The
curve becomes very, very close to the asymptote line,
but never touches it.
vertical asymptote x = – 3
8
Example:
y
6
4
2
horizontal asymptote y = 0
x
–8 –6 –4 –2
2
–2
–4
–6
–8
4
6
8
Yesterday we grouped the following equations:
cubic
reciprocal
exponential
y  x3
1
y
x
1
y  4
x
y  2x
y  (x  1)3
y  (x  2)3  1
1
y  (x  2)3
2
1
y
x 3
1
y
1
x3
y  2x  4
y  2(x3)
y  2(x4)  3
Today we will look at reciprocal functions. Be sure to have a
graphing calculator.
Group name: _______________ Functions
1
y
x (parent graph)
Equation: _____
(0, 0)
locator point: _____
x=0
y
x
y
-4
-0.25
8
-3
-0.33 Locator point
6
-2
-0.5
-1
-1
0
ERR
1
1
–2
2
0.5
–4
3
0.33
4
0.25
10
(0, 0)
4
2
–10 –8 –6 –4 –2
y=0
2
4
6
8 10
x
–6
–8
–10
Link to Geo Sketch
1
y  4
x
Equation: ________
x=0
x
y
-4
-4.25
8
-3
-4.33
6
-2
-4.5
4
-1
-5
Locator point
(0, -4)
0
ERR
–10 –8 –6 –4 –2
1
-3
–4
2
-3.5
–6
3
-3.67
–8
4
-3.75
–10
(h, k)
(0, –4)
locator point: _____
y
10
2
2
–2
4
6
8 10
x
y = -4
Link to Geo Sketch
1
y
x3
Equation: ________
x
y
-2
-0.2
-1
-0.25
0
-0.33
1
-0.5
(h, k)
(3, 0)
locator point: _____
y
x=3
10
8
Locator point
6
(3, 0) 4
2
–10 –8 –6 –4 –2
y=0
2
2
-1
3
ERR
–4
4
1
–6
5
0.5
–8
6
0.33
4
6
8 10
x
–2
–10
Link to Geo Sketch
1
y
1
x3
Equation: ________
(h, k)
x = –3 locator point: _____
(–3, 1)
y
x
-4
y
10
0
8
-3
-2
ERR Locator point
6
2
4
-1
0
1.5
1
2
1.25
–4
1.2
–6
3
4
1.166
–8
1.429
–10
1.33
(–3, 1)
2
–10 –8 –6 –4 –2
y=1
2
4
6
8 10
x
–2
Link to Geo Sketch
PARENT GRAPH TOOLKIT
10
Name: Reciprocal
x
1
Parent Equation: y = x
-3 -13
-2 -12
Description of Locator:
-1 -1
intersection of asymptotes (h, k) 0
1
General Equation:
2



y  a 1   k
x h 




3
y
1
2
1
3
horizontal asymptote
y=k
6
4
2
(0, 0)
–4 –2
(–1, –1)–2
(1, 1)
2
4
–4
–6
–8
Properties:
vertical asymptote
x=h
8
y=0
1
y
–10
Domain:
Range:
{x| x  h}
{y| y  k}
   , h   (h,  )
x=0
   , k   (k ,  )
x
Based on the patterns you have observed, graph
the next 4 reciprocal functions on the worksheet
WITHOUT using a graphing calculator.
y
10
8
1
y  6
x
6
4
1
y
x4
1
y
2
x5
1
y
4
x2
2
–10 –8 –6 –4 –2
2
–2
–4
–6
–8
–10
4
6
8 10
x