1. 4.6(a) Notes: Graph of the Tangent Function
Date:
4.6(a) Notes: Graph of the Tangent Function
Lesson Objective: To understand the graph of y = tan x and its variations.
CCSS: F-TF Extend the domain of tri­go­no­me­tric functions using the unit circle.
You will need: Colored pens

2. Lesson 1: The Graph of Tangent
Graph y = tan x for -π/2 ≤ x ≤ π/2 on a coor­­dinate plane. Use red ink for this first graph.   

3. x Lesson 1: The Graph of Tangent – y = tan x Deg. ° y=tan x 3 4 6 π -π   x -π 2
-5π 12 3 4 6 π 5π
Deg. °
y=tan x

4. Lesson 1: The Graph of Tangent   

5. Lesson 1: The Graph of Tangent Observations: 1. Domain: 2. Range:
Observations:
1. Domain:
2. Range:
3. Period:
4. Odd or Even Function?:
5. Vertical Asymptotes:
6. x-int:
7. y = 8.   

6. Lesson 2: The Graph of Tangent – The Shortcut!
Graphing y = A tan (Bx – C):
A. Asymptotes: Bx – C = -π/2 and Bx – C = π/2
B. x-intercept: Midpoint between asymptotes
x = -Asymp.+ Asymp. 2
C. y = -A: Midpt between left asymp and x-int
x = -Asymp.+ x-int. ; y = -A
D. y = A: Midpt btwn x-int and right asymp
x = x-int.+ Asymp. ; y = A   

7. Lesson 2: Graphing y = A tan Bx
Graph y = 3 tan 2x in blue ink for -π/4 ≤ x ≤ 3π/4 on the same coor­dinate plane from Lesson 1.   

8. = Asymp: Bx – C = -π/2 Bx – C = π/2 x-intercept: x = + = 2 y = -A:
Lesson 2: Graphing y = 3 tan 2x
Asymp: Bx – C = -π/ Bx – C = π/2
x-intercept: x = = 2
y = -A:
x = =
y = A:
x =
   =

9. Lesson 2: The Graph of Tangent – The Shortcut!
Graph y = 3 tan 2x in blue ink for -π/4 ≤ x ≤ 3π/4 on the same coor­dinate plane from Lesson 1.   

10. Lesson 3: Graphing y = tan (Bx – C)
Graph two full periods of y = tan (x – π/2) in purple or black ink on the same coor­dinate plane from Lessons 1 and 2.   

11. = Asymp: Bx – C = -π/2 Bx – C = π/2 x-intercept: x = + = 2 y = -A:
Lesson 2: Graphing y = tan (x – π/2)
Asymp: Bx – C = -π/ Bx – C = π/2
x-intercept: x = = 2
y = -A:
x = =
y = A:
x =
   =

12. Lesson 3: Graphing y = tan (Bx – C)
Graph two full periods of y = tan (x – π/2) in purple or black ink on the same coor­dinate plane from Lessons 1 and 2.   

13. 4.6(a): Do I Get It? Yes or No
1. Graph y = 2 tan x/2 over -π < x < 3π.
2. Graph two full periods of y = tan (x + π/4).