Question

Write the equation of the function please help

Answer 1

Examine the graph.

The graph looks like one of square-root....let'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