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):

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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),

.

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

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