MTH405_Wk_5_Lect_1 - MTH405 Wk 5 Lect 1 Trigonometric...

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Unformatted text preview: MTH405 Wk 5 Lect 1 Trigonometric Function Functions of the form y = A sin(Bx + C) + D or y = A cos(Bx + C) + D. The importance of A, B, C, D are: • A is the amplitude of the graph • B is the number of cycles that the function has within 360◦ or 2π radians. • C is the horizontal shift of the graph (+C shifts left, −C shifts right) • D is the vertical shift of the graph (+D shifts up, −D shifts down) The procedure to graph a trigonometric function is to: • nd A, B, C, D • draw a dashed generic graph for reference (if sin graph, then draw y = sin x and if cos graph, then draw y = cos x ) • Then use A, B, C, D to draw the actual graph Example. Draw the following graphs. 1. y = 2 sin x 2. y = 2 sin 2x 3. y = 3 cos(x + 45◦ ) 1 Exponential Function Functions of the form y = AeBx . The importance of A and B are: • A is the multiplying factor for the part eBx . • B determines the steepness of the graph as x becomes positive. If B is positive, then we have a positive graph, but if B is negative, then we have a negative graph. The procedure to graph an exponential function is to : • nd A and B . • draw a dashed generic graph for reference (draw y = ex ) • Then utilise A and B to draw the actual graph. Example. Draw the following graphs. 1. y = ex 2. y = 2ex 3. y = e2x 4. y = e−x 5. y = e−2x 2 Basic Logarithmic Function These are functions of the form y = ln(x + A) + B. Example. Draw the following functions. 1. y = ln x 2. y = ln |x| 3. y = 2 ln x 4. y = ln(x + 2) Basic Alsolute Value Function These are functions of the form y = |x + A| + B. Example. Draw the following functions. 1. y = |x| 2. y = 2 · |x| 3. y = |x + 2| 4. y = |x − 3| + 1 Basic Square Root Function These are functions of the form y= Example. 1. y = 2. 3. 4. 5. 6. √ x + A + B. Draw the following functions. √ x (In reality, this is not a function) √ y=+ x √ y=− x √ y = x + 2 (having no + or − sign infront, then by default, we take it to be +) √ y = x−3 √ y = x−1+1 3 ...
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