# Starter Draw the graph of y logx1 for

• Slides: 10

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

+ 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

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

+ 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

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

+ Investigation 1: Using technology plot the following: y = sinx y = 3 sinx y = 0. 5 sinx For each graph: u Find the maximum and minimum value u Find the period and amplitude Describe the effect of a in the function y = asinx u What is the amplitude of: y = 4 sinx y = ⅔sinx

+ Investigation 2: Using technology plot the following: y = cosx y = cos 2 x y = cos(0. 5 x) For each graph: u Find the maximum and minimum value u Find the period and amplitude Describe the effect of b in the function y = cosbx u What is the period of: y = cos 4 x y = cos¼x

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

+ IN GENERAL: y = Asin. Bx + C Affects Amplitude Affects Period To find: ² ² Period = 360/B Principal axis y = C Affects Principal Axis

+ Examples: Sketch the following graphs: ² ² ² y = 2 sinx + 4 y = -3 sin 2 x y = sin(0. 5 X) - 2 Find for each graph: Maximum Minimum Amplitude Principal Axis Period