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Functions

Functions. Transformation of Functions. AIM: Transform a parent function in order to sketch a function. Remember. Identify the functions of the graphs below:. Square Root. Absolute Value. Q uadratic. Linear. f (x) = x. f (x) = | x |. f (x) =. f (x) = x 2.

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Functions

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  1. Functions Transformation of Functions

  2. AIM: Transform a parent function in order to sketch a function. Remember • Identify the functions of the graphs below: Square Root Absolute Value Quadratic Linear f(x) = x f(x) = |x| f(x) = f(x) = x2

  3. AIM: Transform a parent function in order to sketch a function. Transformed • Each of the prior graphs are called parent functions • We can use a parent function to quickly sketch ‘babies’ f(x) = x f(x) = |x| f(x) = f(x) = x2

  4. AIM: Transform a parent function in order to sketch a function. Translation • Each parent function can slide f(x) = x2 - 3 f(x) = (x + 3)2 f(x) = x2 f(x) = x2 f(x) = x2 + 3 f(x) = (x - 3)2

  5. AIM: Transform a parent function in order to sketch a function. SLIDE THE FUNCTION y = ( x+ c) + d VERTICAL SHIFT + up - down HORIZONTAL SHIFT +left -right

  6. AIM: Transform a parent function in order to sketch a function. Reflection • Each parent function can flip f(x) = √-x f(x) = √x f(x) = √x f(x) = - √x

  7. AIM: Transform a parent function in order to sketch a function. Flip THE FUNCTION y = -(-x+ c) + d REFLECT over the x axis VERTICAL SHIFT + up - down HORIZONTAL SHIFT + down - up REFLECT over the y axis

  8. AIM: Transform a parent function in order to sketch a function. Dilation • Each parent function can change size f(x) = 0.5x2 f(x) = (0.5x)2 f(x) = x2 f(x) = x2 f(x) = (2x)2 f(x) = 2x2

  9. AIM: Transform a parent function in order to sketch a function. Stretch THE FUNCTION y = - a (-bx+ c) + d REFLECT over the x axis VERTICAL a > 1 stretches 0 < a < 1 flattens VERTICAL SHIFT + up - down HORIZONTAL SHIFT + left - right REFLECT over the y axis HORIZONTAL b > 1 narrow 0 < b < 1 widens

  10. AIM: Transform a parent function in order to sketch a function. TRY • Describe f(x) = -2(x + 3)2 - 1 f(x) = (x + 3)2 f(x) = x2 f(x) = 2(x+3)2 a parabola that shifts to the left 3 units, is stretched vertically by a factor of 2, flipped over the x axis, and brought down 1 unit. f(x) = -2(x+3)2 f(x) = -2(x+3)2

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