Draw a graph of volume versus time

Reference no: EM132303088

Functions Assignment Questions -

Q1. State whether the following functions are periodic or not.

Q2. For each function above that is periodic, state the period and amplitude of the function.

Q3. A periodic function f(x) has a period of 8. The values of f(1), f(5), and f(7) are -3, 2, and 8, respectively. Predict the value of each of the following. If a prediction is not possible, explain why not.

a) f(9)

b) f(29)

c) f(63)

d) f(40)

Q4. Sketch the graph of a periodic function with an amplitude of 8 and a period of 5. Explain why your function is periodic.

Q5. Sketch the following graphs:

a) y = 3 sin[2(x - 30^o)] - 2

b) y = -2 cos[½(x + 45^o)] + 1

Q6. Let f(x) = 3 cos[3(x - 37^o)] + 5. State the amplitude, period, phase shift, and equation of the axis.

Q7. Write an equation for the sine function with the following characteristics:

Amplitude: 5

Period: 90^o

Phase Shift: 72^o to the left

Equation of the Axis: y = -9

Q8. Write the equation of the following function:

Q9. The volume of air in the lungs during normal breathing can be modelled by a sinusoidal function of time. Suppose a person's lungs contain from 2200mL to 2800mL of air during normal breathing. Suppose a normal breath takes 4 seconds, and that t = 0s corresponds to a minimum volume.

a) Let V represent the volume of air in a person's lungs. Draw a graph of volume versus time for 20 seconds.

b) Write an equation of a sinusoidal function to represent this relation.

c) Describe how the graph would change if the person breathes more rapidly. Explain your answer.

d) Describe how the graph would change if the person took bigger breaths. Explain your answer.

Reference no: EM132303088

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