Which function is represented by the graph? f(x) = –|x| 4 f(x) = –|x| – 4 f(x) = –|x 4| f(x) = –|x – 4|.

The linear function has the highest power of the unknown variable one. Thus, the graph plotted for the linear function is a straight line.

Types of function movement over the graph -

Horizontal shift- Let the parent function is [tex]f(x)[/tex]. Thus by replacing parent function with [tex]f(x-b)[/tex] shifts the graph b units right and by replacing parent function with [tex]f(x+b)[/tex] shifts the graph b units left.

Vertical shift- Let the parent function is [tex]f(x)[/tex]. Thus by replacing parent function with [tex]f(x)-c[/tex] shifts the graph b units down and by replacing parent function with [tex]f(x)+c[/tex]shifts the graph b units up.

The graph given in the problem is attached below. All the parents function of the options are absolute function.

In the graph, the parent function 4 units shifted to right. So the -4 should add in the parent function. Thus, by the above definition, this is a horizontal shift of the function and can be written as,

[tex]f(x)=-|x-4|[/tex]

Hence, the function which is represented by the graph attached below shifted 4 units right is similar to option d, which is,

[tex]f(x)=-|x-4|[/tex]

Learn more about the graph of linear function here;

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