Question

In this lesson, you learned how to transform square-root functions. Transformations may be: reflection (across the x- or y-axis); translation (horizontal or vertical); stretch (horizontal or vertical); or compression (horizontal or vertical). Suppose you start with a parent function f(x) = √x. Which of the four transformations is easiest for you to represent and which is the most difficult? Why? Give an example of a "child" of the parent function. Make sure you identify the transformation so your reader knows exactly what happened and include the words vertical or horizontal, if necessary.

Answer 1

Let us take a function y=f(x). assuming limit of function exist (rectangular coordinate)

1. Horizontal shifting: y=f(x-a) where a is constant
this shifts curve to the the left by a units
y=f(x+a)
this shift curve to the right by a units.

2. Vertical shifting:
y=f(x)+a
shift curve to the negative y axis by a unit
y=f(x)-a
shift curve to the positive y axis by a unit.

3.horizontal stretching
take a non zero quantity
y=f(x/a)
this stretch the curve in horizontal direction
4. horizontal compressing
y= f(ax)
this compress curve in horizontal by a factor

5. vertical stretching
y=af(x)
this stretch curve in vertical
6. vertical compressing'
y=f(x)/a
this compress curve in vertical

7.y=x line gives the inverse of the function
for inverse just replace x by y

Answer 2

I hope this helps : )