1. Assignment, pencil red pen, highlighter, GP notebook, graphing calculator
U4D7
Have out:
Bellwork:
Graph each function on the same set of axes. Be sure to identify the inflection point. 2 4 6 8 10 y x –2 –4 –6 –8
–10
f(x) = (x + 4)3 – 2
f(x) = (x + 4)3 – 2
inflection point:
(–4, –2) +1 +3 +3
inflection point:
(5, 3) +1
total:

2. Asymptote Recall: Asymptote: Example:
PG – 77
Asymptote
Recall:
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 2 4 –2 –4 6 8 –6 –8 x y
Example:
horizontal asymptote y = 0

3. Done Yesterday we grouped the following equations: cubic reciprocal
exponential
Done
Today we will look at reciprocal functions. Be sure to have a graphing calculator.

4. Reciprocal Locator point (0, 0) Group name: _______________ Functions
(parent graph)
(0, 0)
Equation: _____
locator point: _____
x = 0 x y -4
-0.25 -3
-0.33 -2
-0.5 -1
ERR 1 2
0.5 3
0.33 4
0.25 x y -4 -3 -2 -1 1 2 3 4 2 4 6 8 10 y x –2 –4 –6 –8
–10
Locator point
(0, 0)
y = 0
Link to Geo Sketch

5. (h, k)
(0, –4)
Equation: ________
locator point: _____
x = 0 x y -4
-4.25 -3
-4.33 -2
-4.5 -1 -5
ERR 1 2
-3.5 3
-3.67 4
-3.75 x y -4 -3 -2 -1 1 2 3 4 2 4 6 8 10 y x –2 –4 –6 –8
–10
Locator point
(0, -4)
y = -4
Link to Geo Sketch

6. (h, k)
(3, 0)
Equation: ________
locator point: _____ x y -2
-0.2 -1
-0.25
-0.33 1
-0.5 2 3
ERR 4 5
0.5 6
0.33 x y -2 -1 1 2 3 4 5 6 2 4 6 8 10 y x –2 –4 –6 –8
–10
x = 3
Locator point
(3, 0)
y = 0
Link to Geo Sketch

7. (h, k)
x = –3
(–3, 1)
Equation: ________
locator point: _____ x y -4 -3 -2 -1 1 2 3 4 x y -4 -3
ERR -2 2 -1
1.5
1.33 1
1.25
1.2 3
1.166 4
1.429 2 4 6 8 10 y x –2 –4 –6 –8
–10
Locator point
(–3, 1)
y = 1
Link to Geo Sketch

8. PARENT GRAPH TOOLKIT x y -3 -2 -1 1 2 3 x y Name: Reciprocal10 x y -3 -2 -1 1 2 3 x y
Name:
Reciprocal 8
Parent Equation: 6 4
Description of Locator: 2
(1, 1)
y = 0
(0, 0) x
intersection of asymptotes
(h, k) –4 –2 2 4
(–1, –1) –2
General Equation: –4 –6 –8
Properties:
–10
x = 0
vertical asymptote
Domain:
Range:
x = h
{x| x  h}
{y| y  k}
horizontal asymptote
y = k

9. Based on the patterns you have observed, graph the next 4 reciprocal functions on the worksheet WITHOUT using a graphing calculator. 2 4 6 8 10 y x –2 –4 –6 –8
–10

10. Finish today's assignment:
PG & worksheets