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42 votes
42 votes
What is the effect on the graph of f(X) = |X| when the function is changed to

g(X) = -2|x|?
OA. The graph is reflected across the x-axis and stretched vertically by
a factor of 2.
O B. The graph is shifted to the left 2 units.
C. The graph is shifted down 2 units.
D. The graph is reflected across the x-axis and compressed vertically
by a factor of 2.

User Anthony Pham
by
2.2k points

1 Answer

28 votes
28 votes

Answer:

A. The graph is reflected across the x-axis and stretched vertically by

a factor of 2.

Explanation:

Transformations

For a > 0


f(x+a) \implies f(x) \: \textsf{translated $a$ units left}.


f(x-a) \implies f(x) \: \textsf{translated $a$ units right}.


f(x)+a \implies f(x) \: \textsf{translated $a$ units up}.


f(x)-a \implies f(x) \: \textsf{translated $a$ units down}.


a\:f(x) \implies f(x) \: \textsf{stretched parallel to the $y$-axis (vertically) by a factor of $a$}.


f(ax) \implies f(x) \: \textsf{stretched parallel to the $x$-axis (horizontally) by a factor of $(1)/(a)$}.


-f(x) \implies f(x) \: \textsf{reflected in the $x$-axis}.


f(-x) \implies f(x) \: \textsf{reflected in the $y$-axis}.

Given functions:


f(x)=|x|


g(x)=-2|x|

The series of transformations that take function f(x) to function g(x) are:

1. Reflection across the x-axis:


-f(x)\implies g(x)-|x|

2. Vertical stretch by a factor of 2:


-2f(x) \implies g(x)=-2|x|

User Annakata
by
2.7k points
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