Picture Write the equations based on the vertical translations listed from f(x). The new equation is k(x).
f(0) = 2x - 3
Vertical translation up 3 units. k(x)=
Vertical translation down 4 units. k(x)=1
Vertical translation up 2 units. k(x)=
Vertical translation down 5 units. k(x)=1

9514 1404 393

Step-by-step explanation:

Vertical translation adds the amount of upward translation to the value of the function. Upward translation by 'v' units will make the new function ...

  k(x) = f(x) +v

__

We assume your f(x) is 2x -3.

Up 3 units

  k(x) = f(x) +3 = 2x -3 +3

  k(x) = 2x

Down 4 units

  k(x) = f(x) -4 = 2x -3 -4

  k(x) = 2x -7

Up 2 units

  k(x) = f(x) +2 = 2x -3 +2

  k(x) = 2x -1

Down 5 units

  k(x) = f(x) -5 = 2x -3 -5

  k(x) = 2x -8

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!