**Transformations of Functions--Quiz**

**Problem 1.**
** **
Below you have the graph of the function

** .**

The graph of y=g(x) :

Find a possible formula for each of the three graphs (a), (b), (c) given below.

The graph (a):

The graph (b):

The graph (c):

`> `

**Answer: **
** **
(a) is the graph of y=-g(x), that is, of the function
** **
. Indeed, the graph (a) is a reflection of the graph y=g(x) about the x-axis.

(b) is the horizontal translation of y=g(x) two units to the right. Hence, the formula is y=g(x-2); that is:

** .**

(c) is a vertical stretch of the graph y=g(x) by the factor of 2. Hence the formula is y=2g(x),

** .**

`> `

*MTH 111 Quizzes, B. Kaskosz, L.Pakula, 2001.*

`> `