1. Starter
Draw the graph of y = log(x+1) for -6≤ x ≤ 14. Draw in the asymptote
Asymptote is at x = -1

2. Note 9: Periodic Functions
Periodic Function A function that repeats itself over and over is a horizontal direction. Period of a Function The length of one repetition of the function. Principal Axis The horizontal line that the function oscillates about. Principal axis = maximum + minimum 2

3. Amplitude The vertical distance from the principal axis to the maximum or to the minimum point. Amplitude = maximum – minimum 2

4. Note 10: Sine and Cosine Curve
Draw an accurate sketch of the Sine and Cosine Curve: x-axis from 0° to 360° - plot every 30° y-axis from -1 to 1 – plot every 0.25

5. Characteristics of the Sine and Cosine Curve
The period is 360°
The amplitude is 1
The maximum value is 1 and minimum value is -1
The domain is: 0° < x < 360°
The range is: -1 < y < 1
The cosine curve is just the sine curve shifted by 90°

6. Investigation 1:
Using technology plot the following:
y = sinx
y = 3sinx
y = 0.5sinx
For each graph:
Find the maximum and minimum value
Find the period and amplitude
Describe the effect of a in the function y = asinx
What is the amplitude of:
y = 4sinx y = ⅔sinx

7. Investigation 2:
Using technology plot the following:
y = cosx
y = cos2x
y = cos(0.5x)
For each graph:
Find the maximum and minimum value
Find the period and amplitude
Describe the effect of b in the function y = cosbx
What is the period of:
y = cos4x y = cos¼x

8. Investigation 3:
Using technology plot the following:
y = sinx + 2
y = sinx – 1
For each graph:
Find the maximum and minimum value
Find the period and amplitude
Calculate the equation of the principal axis
What is the connection between:
y = sinx
y = sinx + c

9. IN GENERAL: y = AsinBx + C To find: Period = 360/B
Principal axis y = C
Affects
Amplitude
Affects
Period
Affects
Principal Axis

10. Sketch the following graphs:
Examples:
Sketch the following graphs:
y = 2sinx + 4
y = -3sin2x
y = sin(0.5X) - 2
Find for each graph:
Maximum
Minimum
Amplitude
Principal Axis
Period