Precalculus A



Precalculus A Name

5.4 - 5.6 PRE-TEST – NO GRAPHING CALCULATORS

1. Explain how each letter impacts the graph if each letter is greater than zero.

y = A sin(Bx + C) – D y = -E cos(x – F) + G

A -

B -

C -

D -

E -

F -

G -

Write the equation of a sine function that has the given characteristics.

2. Amplitude = ½ Period = 2/5 Phase Shift = 2 y =

3. Amplitude = 4 Period = π/4 Phase Shift = -3π/8 y =

4. Amplitude = 1/5 Period = 6 Phase Shift = 1/3 y =

5. Amplitude = 1 Period = π/3 Phase Shift = -1/6 y =

Determine the amplitude/vertical stretch, period and phase shift for each function without graphing.

6. y = 3 sin(4/5 x - 5π/8) A = T = Phase Shift =

7. y = 1/2 sec(1/2x) A = T = Phase Shift =

8. y = -2 cos(8/3 x + 4π/5) A = T = Phase Shift =

9. y = 2 tan(3x) A = T = Phase Shift =

10. y = 3 csc(2x) A = T = Phase Shift =

11. y = cot(x + π/2) A = T = Phase Shift =

Determine the amplitude/vertical stretch, period and phase shift for each function.

Graph two complete cycles of each function. Label your axes.

12. y = 5sin(4πx + 3π)

Amplitude =

Period =

Phase Shift =

13. y = -3tan(π/2 x)

Amplitude =

Period =

Phase Shift =

14. y = -2sec(x – π/2)

Amplitude =

Period =

Phase Shift =

15. y = 3/2cos(1/2 x + π)

Amplitude =

Period =

Phase Shift =

16. y = 4cot(1/3 x)

Amplitude =

Period =

Phase Shift =

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