Answer:
The function [tex]f(x)=\sqrt{x+2}[/tex] is shown by the graph below ⇒ 2nd answer
Step-by-step explanation:
To find the right function chose two points from the graph and substitute the x-coordinate of each point in the function to find the y-coordinate, if they are the same with the corresponding y-coordinates of the points, then the function is shown by the graph
From the figure:
The curve passes through points (-2 , 0) and (2 , 2)
∵ [tex]f(x)=\sqrt{x-2}[/tex]
∵ x = -2
- Substitute x by -2
∴ [tex]f(-2)=\sqrt{-2-2}[/tex]
∴ [tex]f(-2)=\sqrt{-4}[/tex] ⇒ it is impossible no square root for (-) number
∴ [tex]f(x)=\sqrt{x-2}[/tex] is not the function shown by the graph
∵ [tex]f(x)=\sqrt{x+2}[/tex]
∵ x = -2
- Substitute x by -2
∴ [tex]f(-2)=\sqrt{-2+2}[/tex]
∴ [tex]f(-2)=\sqrt{0}[/tex]
∴ f(-2) = 0 ⇒ same as the y-coordinate of x = -2
∵ x = 2
- Substitute x by 2
∴ [tex]f(2)=\sqrt{2+2}[/tex]
∴ [tex]f(2)=\sqrt{4}[/tex]
∴ f(2) = 2 ⇒ same as the y-coordinate of x = 2
∴ The function [tex]f(x)=\sqrt{x+2}[/tex] is shown by the graph below
