Interactive notes 5.1
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Trigonometric functions are periodic, meaning their graphs repeat at regular intervals. The period is the smallest number of units that must be traveled along the horizontal axis for the graph to repeat. Amplitude is defined as the maximum value of the function minus the minimum value, and represents half the peak-to-peak variation in the graph. For functions centered around the horizontal axis, the amplitude is simply the maximum height above this axis. Two examples are given to illustrate calculating the period and amplitude of trigonometric functions.
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3
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The height,
h,
of a projectile is a function of the time,
t,
it is in the air. The height in meters for
t
seconds is given by the function h(t)= -9.8t2+19.6t. What is the domain of the function? What does the domain mean in the context of the problem?
SECTION 3.3
Algebraic
For the following exercise, find the average rate of change of each function on the interval specified in simplest form.
k(x)=23x+1
on [2, 2+h]
Graphical
For the following exercise, use the graph of each function to
estimate
the intervals on which the function is increasing or decreasing.
For the following exercise, find the average rate of change of each function on the interval specified.
g(x)=3x2-23x3 on [1, 3]
Real-World Applications
Near the surface of the moon, the distance that an object falls is a function of time. It is given by d(t)=1.6t2, where
t
is in seconds and d(t) is in meters. If an object is dropped from a certain height, find the average velocity of the object from t = 2 to t = 5.
SECTION 3.4
Algebraic
For the following exercise, determine the domain for each function in interval notation. (4 points)
f(x)=2x+5 and g(x)=4x+9, find f-g, f+g, fg, and fg
For.
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Introduction to objective, scope and outcome the subject
Chapter 2
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Chapter 6
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Interactive notes 5.1
- 1. 1 BUM1113 Technical Mathematics Dr Norazaliza Mohd Jamil September 2018 Chapter 5: Graphs of the Trigonometric Functions 5.1 Trigonometric Functions: periods Periodic function: the graphs display patterns that repeat themselves at regular intervals. A function f is said to be periodic if there is a number 0 p such that ( ) ( ) f x p f x . The smallest such number p is called the period of f . Examples of periodic function: sin( 2 ) sin x x cos( 2 ) cos x x The period represents the minimum number of units that we must travel along the horizontal axis before the graph begins to repeat itself. Let f be a periodic function and let m an M denote the minimum and maximum values of the function. Then, the amplitude of f is the number 2 M m A . Amplitude is always positive. For a function in which the graph is cantered about the horizontal axis, the amplitude is simply the maximum height of the graph above the horizontal axis.
- 2. 2 BUM1113 Technical Mathematics Dr Norazaliza Mohd Jamil September 2018 Example Specify the period and amplitude. Period = 2 Amplitude: 4 ( 4) 4 2 A 1. 2. 3. Example Specify the period and amplitude. Period 6 Amplitude: 4 2 1 2 A 4. 5. 6.
- 3. 3 BUM1113 Technical Mathematics Dr Norazaliza Mohd Jamil September 2018 Exercises 5.1: 1. Specify the period and amplitude for each function. (a) (b) (c) (d)
- 4. 4 BUM1113 Technical Mathematics Dr Norazaliza Mohd Jamil September 2018 (e) (f) (g)