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MATH SL1 - UNIT 4 Functions & Transformations Name: Date: D. TRANSFORMATIONS OF FUNCTIONS (pg. 53-65) D.1 Parent functions First we need to look at a number of functions, some continuous and some discontinuous. Task 1: 1. 2. 3. 4. Sketch a graph of each parent function. State the type of function it is. State the domain and range. State the equations of any asymptotes. a) f ( x) = c b) f ( x) = x c) f ( x) = x e) f ( x) = x f) f ( x) = x3 g) f ( x) = 1 x d) f ( x) = x 2 h) f ( x) = 1 x2 D.2 Transformations of functions Now it is time to investigate how you can transform (change) these parent functions graphs. A very useful tool when you are trying to model real-life phenomena. You can literally (almost) bend functions to your will. When you investigate, you will want to use some of the following words and notations to describe what you see and observe: horizontal, vertical, reflection, translation, dilation, shift, shrink, asymptote, domain, range, ⎛x⎞ and the notation ⎜ ⎟ to describe movement in the x or y direction (no movement = 0) ⎝ y⎠ 1 Task 1: Investigate y = f ( x − h) and y = f ( x) + k 1. Use the 8 different types of functions below to really verify a consistent behavior. 2. Sketch 2+ graphs on one small coordinate plane a) f ( x) = c b) f ( x) = x c) f ( x) = x e) f ( x) = x f) f ( x) = x3 g) f ( x) = 1 x d) f ( x) = x 2 h) f ( x) = 1 x2 General rule for all transformations of the form y = f ( x − h) and y = f ( x) + k : Task 2: Investigate y = − f ( x) and y = f (− x) 1. Use the 8 different types of functions below to really verify a consistent behavior. 2. Sketch 2 graphs on one small coordinate plane a) f ( x) = c b) f ( x) = x c) f ( x) = x d) f ( x) = x 2 2 e) f ( x) = x f) f ( x) = x3 g) f ( x) = 1 x h) f ( x) = 1 x2 General rule for all transformations of the form y = − f ( x) and y = f (− x) : Task 3: Investigate y = af ( x) and y = f (bx) 1. Use the 8 different types of functions below to really verify a consistent behavior. 2. Sketch 2+ graphs on one small coordinate plane a) f ( x) = c b) f ( x) = x c) f ( x) = x e) f ( x) = x f) f ( x) = x3 g) f ( x) = 1 x d) f ( x) = x 2 h) f ( x) = 1 x2 3 General rule for all non-rigid transformations of the form y = af ( x) and y = f (bx) : Homework: Read the summary on page 64 then do Ex 2.4 #1,5,9,11,15,16,17,18,19acdef,23 4