Complete the function table for each equation Part A and Part Bthen discuss how did get these

A)

We have the function

Look that on the table we have the values of x, and we must complete the table for the values of y.

To do it we just have to put the value of x and simplify the expression, let's do it for x = 5, the first line:

1 Step: Change "x" for the value you want to do

We're doing with 5 now, then let's put 5 instead of x.

2 Step: Do all the calculus

Then that line we have

Let's repeat the process for -6:

Then on the second line we have x = -6 and y = 41

Doing the same thing for -1:

Let's put it on the table

Repeat the process for x = -4

Updating the table:

And the last one, x = -3, does the same process

And we have our table complete

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!