Precalculus/Trig 3
Trig Graphs Test Review
Name ____________________________________
State the following information for each equation. If it is not applicable, write none.
a) Amplitude
b) Period
c) Asymptotes
d) Reflections
e) Vertical Shifts
f) Phase Shifts
g) Domain

)+2
4

4. y = 2 tan (2x - ) + 2
2
1. y = sin(x -
h) Range

)–1
3
3

5. y = -3sin
(x + ) –1
2
2
3. y = -tan x – 1
2. y = 2cos 2(x -
6. y = cos (3x -  ) – 1
Use the following information to write an equation of the graph described:
7. sin; Amp = 2, per =  , vertical shift = down 3.

8. cos; Amp = 1; per = , phase shift = left  .
4
9. tan; Vertical stretch of 3; per = 2 , phase shift = right
2
.
3
2

; phase shift = right ; vertical shift = up 3; reflect over x-axis.
3
4
3 3
 k ; NO phase shift; vertical shift = up 1.
11. tan; vertical stretch of 2; Vertical asymptotes at
4 2
10
12. cos; Amp = 2, period of
, reflect over x-axis.
3
10. sin; Amp = 4, per =
Write one sine and one cosine equation for each graph below.
13.
14.
Sketch 2 periods of each of the following graphs. Be sure to list key information first.
1. y = sin x
Amp:
Period:
Domain:
Range:
Vertical Asymptotes:
2. y = cos x
Amp:
Period:
Domain:
Range:
Vertical Asymptotes:
3. y = tan x
Amp:
Period:
Domain:
Range:
Vertical Asymptotes:
4. y = csc x
Amp:
Period:
Domain:
Range:
Vertical Asymptotes:
5. y = sec x
Amp:
Period:
Domain:
Range:
Vertical Asymptotes:
6. y = cot x
Amp:
Period:
Domain:
Range:
Vertical Asymptotes:
x
7. y  csc  2
3
Amp:
Period:
Domain:
Range:
Vertical Asymptotes:
8. y = 2cos 2(x -

)–1
3
Amp:
Period:
Domain:
Range:
Vertical Asymptotes:
9. y  2sec 2 x  1
Amp:
Period:
Domain:
Range:
Vertical Asymptotes:
10. y = 2 tan (2x -

)+2
2
Amp:
Period:
Domain:
Range:
Vertical Asymptotes:
11. y = -3sin
3

(x + ) –1
2
2
Amp:
Period:
Domain:
Range:
Vertical Asymptotes:
12. y = cos (3x -  ) – 1
Amp:
Period:
Domain:
Range:
Vertical Asymptotes: