Question

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

Answer 1

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

the v shape comes from |x| shifted up from the origin by 2.5

Answer 2

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.