Question

!!!!PLEASE HELP!!!

Functions f(x) and g(x) are defined below.

`f(x)=-√(x+2) -3\\g(x)=-2|x-3|+4`
Determine where f(x) = g(x) by graphing.

A. x ~-6.2 ; x = -4
B. x = -4 ; x = -1
C. x = -1 ; x ~8.1
D. x ~-6.2 ; x ~8.1

Answer 1

C. x = -1 ; x ~8.1

Explanation:

First we graph
`f(x)= -√(x+2) -3`

Here we have x+2 under the square root. x+2>=0, x>=-2

So we take some x values greater than -2 and find out f(x) to make a table for graphing

x f(x)

-2
`-√(-2+2) -3=-3`

-1 -4

2 -5

Graph it and extent the graph

Now we graph
`g(x)= -2|x-3| + 4`

Given equation is in the form of g(x) = a|x-h| + k

where (h,k) is the vertex

here h= 3 and k = 4, so vertex is (3,4)

Now make a table, pick some numbers for x less than and greater than vertex

x y

-1
`-2|-1-3| + 4=-4`

0
`-2|0-3| + 4=-2`

3 4

6 -2

Both graphs are attached below

The graph of f(x) and g(x) interests at x= -1 and x=8.1