 # TRANSFORMATION OF FUNCTIONS FUNCTIONS. REMEMBER Identify the functions of the graphs below: f(x) = x f(x) = x 2 f(x) = |x|f(x) = Quadratic Absolute Value.

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TRANSFORMATION OF FUNCTIONS FUNCTIONS

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

TRANSLATION Each parent function can slide f(x) = x 2 f(x) = x 2 + 3 f(x) = x 2 - 3 f(x) = x 2 f(x) = (x + 3) 2 f(x) = (x - 3) 2 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 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) = √xf(x) = √-x AIM: Transform a parent function in order to sketch a function.

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

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

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

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

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