1.1 Parent Functions and Transformations

Match the following:

Describe the transformation on the parent function: $$f\left(x\right)\ =\ 2\left|x-3\right|-2$$ ​ (a)   ​ (b)   ​ (c)  

Describe the transformation on the parent function: $$f\left(x\right)\ =\ \frac{1}{2}\left(x+3\right)^2$$ ​ ​ (a)   ​ (b)  

Transform the quadratic parent function to show that there is a vertical translation up 4 units, a horizontal translation left 2 units, and vertical reflection.

(Make sure one of the points is on the vertex, and the other a zero.)

What is the equation of the parent function shown in the graph?

Graph the exponential parent function.

What transformations were used to create the function? $$f\left(x\right)=\sqrt[3]{x}+3$$ ​ (a)  

What is the name of the parent function shown: $$f\left(x\right)\ =\ x^3$$

Given the general form to transform any function: a f [ b(x - h) ] + k, what does the a cause the function to do?