Mrs. hyde is the art teacher at washington elementary school. she is hanging her students' artwork on one of the walls in the school hallway. use the clues to determine in which order the artwork is being hung, from left to right. the third graders are to the left of the fourth graders. the second graders are between the fifth graders and the third graders. the fifth graders' artwork is hung first.

1. The fifth graders' artwork is hung first.

2.  The second graders are between the fifth graders and the third graders. Since the fifth graders' artwork is hung first, then the second graders' artwork is hung second and the third graders' artwork is hung third.

3. The third graders are to the left of the fourth graders. This means that the fourth graders' artwork is hung fourth.

5th draders' artwork, 2nd graders' artwork, 3rd graders' artwork, 4th graders' artwork (from the left to the right).

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!