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Which function is represented by the graph?

g(x) = |x + 2.5|
g(x) = |x| + 2.5
g(x) = |x – 2.5|
g(x) = |x| – 2.5

Which function is represented by the graph? g(x) = |x + 2.5| g(x) = |x| + 2.5 g(x-example-1

2 Answers

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the function is
g(x) = |x| + 2.5

the v shape comes from |x| shifted up from the origin by 2.5
User Ernesto Stifano
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7.4k points
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Answer:

The correct option is 2.

Explanation:

The parent absolute function is


f(x)=|x|

The graph of this function is V-shaped and the vertex of this function is origin.

The transformation is defined as


g(x)=|x+a|+b .... (1)

Where, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

From the given graph it is clear that the function shifts 2.5 units up. It means a=0 and b=2.5.

Substitute a=0 and b=2.5 in equation (1).


g(x)=|x+0|+2.5


g(x)=|x|+2.5

The required function is g(x)=|x|+2.5. Therefore the correct option is 2.

User Sency
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8.6k points

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