Write the equation of the function

Examine the graph.

The graph looks like one of square-rootlet's see.

If we make a translation of (-3,-2), i.e. the beginning of the graph, to the origin, we will see that we have the following points on the graph,

(0,0), (1,1), (4,2), (5,2.2), (8,2.8)

all of which correspond to the sqrt(x) function.

Thus if we take the parent graph as sqrt(x), and translate to the current position by a translation of (-3,-2), we get the current graph.

To do the translation, we recall that a translation of a parent function f(x) by (h,k) can be effected by

g(x) ->f(x-h)+k

Setting h=-3, k=-2, and f(x)=sqrt(x), we get

current graph g(x)=f(x-(-3)+(-2)=f(x+3)-2 = sqrt(x+3)-2

option a.

step-by-step explanation:

if you look closely at the graph, we can notice that the function is not defined at two different points.

if you look at functions b and c, you will notice that both functions are not defined at just one point. the function b is not defined at x= -5/2 and function c is not defined at x=-5. both options are discarded, given that our function should not be defined at two fiferent points.

now, if you look closely at the graph you will notice that the function sketched is not defined at x=5 and x=-2.

square root

step-by-step explanation: