Answer:
The graphed function is
[tex]y = \frac{1}{2} x + 2 [/tex]
Step-by-step explanation:
We can simplify all of the functions and see which three of them are the same.
The first one is already simplified.
[tex]f(x) = \frac{1}{5} x - 4[/tex]
The second one is also already simplified.
[tex]\boxed { y = \frac{1}{2} x + 2 }[/tex]
The third one is also already simplified.
[tex]f(x) = \frac{1}{2} x + 1[/tex]
The fourth one is
[tex]y - 3= \frac{1}{2} (x - 2)[/tex]
Expand to get:
[tex]y - 3 = \frac{1}{2}x - 1[/tex]
Add 3 to both sides to get:
[tex]y = \frac{1}{2} x - 1 + 3[/tex]
[tex]\boxed { y = \frac{1}{2} x + 2 }[/tex]
The last option is
[tex]y - 1 = \frac{1}{2}(x + 2)[/tex]
Expand to get:
[tex]y - 1 = \frac{1}{2}x + 1[/tex]
Add 1 to both sides to get:
[tex]y = \frac{1}{2} x + 1 + 1[/tex]
This simplifies to
[tex] \boxed { y = \frac{1}{2} x + 2 }[/tex]
The missing graph is shown in the attachment.
