Answer:
Third option:
Step-by-step explanation:
Graph of functions
The graph shown in the image corresponds to a curved line passing through points (0,2) and (4,4).
Option 1:
[tex]y=\sqrt{x+2}[/tex]
Substituting x=0:
[tex]y=\sqrt{0+2}=\sqrt{2}[/tex]
The point is not (0,2), thus the function is incorrect.
Option 2:
y=x+2
This function corresponds to a straight line with slope 1 and y-intercept 2.
The graph is a curved line, thus the function is incorrect.
Option 3:
[tex]y=\sqrt{x}+2[/tex]
Substituting x=0:
[tex]y=\sqrt{0}+2[/tex]
y=0+2=2
Now test the point x=4:
[tex]y=\sqrt{4}+2[/tex]
y=2+2=4
The point (4,4) also corresponds to the function on the graph. This proof is not conclusive, but since the other options do not match, this is the correct option.
Option 4:
[tex]y=\sqrt{x}-2[/tex]
Substituting x=0:
[tex]y=\sqrt{0}-2[/tex]
y=-2
The point should be (0,2) and not (0,-2). Incorrect function
