Question

What function is shown by the graph below?

Answer 1

Answer:

The function $f(x)=\sqrt{x+2}$  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)

∵  $f(x)=\sqrt{x-2}$

∵ x = -2

- Substitute x by -2

∴ $f(-2)=\sqrt{-2-2}$

∴ $f(-2)=\sqrt{-4}$ ⇒ it is impossible no square root for (-) number

∴ $f(x)=\sqrt{x-2}$ is not the function shown by the graph

∵  $f(x)=\sqrt{x+2}$

∵ x = -2

- Substitute x by -2

∴ $f(-2)=\sqrt{-2+2}$

∴ $f(-2)=\sqrt{0}$

∴ f(-2) = 0 ⇒ same as the y-coordinate of x = -2

∵ x = 2

- Substitute x by 2

∴ $f(2)=\sqrt{2+2}$

∴ $f(2)=\sqrt{4}$

∴ f(2) = 2 ⇒ same as the y-coordinate of x = 2

∴ The function $f(x)=\sqrt{x+2}$ is shown by the graph below