# Graph Transformations: Discovering Manipulating Functions

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Topic:
Functions
Graph Transformations: Discovering How to Manipulate Functions Parent function: a basic function used as the building block for more complicated functions. Some examples of parent functions are: Quadratics (parabolas): f(x)=x^2 (typed x^2) Cubics: f(x)=x^3 (typed x^3) Absolute value: f(x)=|x| (typed abs(x)) Square root: f(x)=√x (typed sqrt(x)) Use the Geogebra worksheet to explore the four functions listed above. Type the parent function you wish to investigate into the input box. Click each of the buttons (yellow, green, blue, and red) one at a time and move the slider left and right to see what different values of the variable do to transform the function. Make sure to check positive and negative integers and rational numbers (decimals). Each colored box will display the transformation function on the graph. The parent function will be visible in blue dotted font and the transformation function will be visible in red font. Complete the exercises below, making conjectures about how the values of each of the variables (a, h, k, and z) transform the parent function.