Question

54322-+Ty-5-4-3-2-1₁2or to w N-3-2 3 4 5 xWhich function is represented by the graph?Of(x) = -x - 3| +4Of(x) = -x +31 +4Of(x) = -x-41 +3Of(x) = -x +41 +3and ExitNextSubm

Answer 1

$f(x)=-\lvert x+4\rvert+3$

1) Note that we need to use as a starting point the parent function f(x)=|x|

2) Examining the graph we can see that the graph is reflected that's why this is necessary to multiply that by -1. In addition to this, we can see that the graph is translated horizontally to 4 units to the left.

And finally, shifted up 3 units. Hence, we can tell that the rule of this absolute value function is:

$f(x)=-|x+4|+3$

And that is the answer.