Investigation on vertical stretch - TRANSFORMATION OF FUNCTIONS(IB/A levels math)

 Consider the function  

1. Identify the intercepts and turning points.

2. Write an expression for 

1. f(2x)
2. f(-2x)
3. f(0.5x)
4. f(-0.1x)

Sketch the above graphs in Q1 to Q4 on the same axes and answer the following

a. Is this a vertical stretch or a horizontal stretch?

b. For the transformation f(px), each point becomes ................. times its original point from y-axis.

c. What is the significance of the sign of p value? 

d. What is the significance of the p-value?

e. The stretch is parallel to ............. axis. 

f. Is there any point that remains invariant in the transformation f(px)?