Question

The graph of a function is shown. Which function is represented by the graph?

Answer 1

The second one : f(x) = x+3, x<0
= 3, x>=0

Answer 2

Answer: The correct option is 2.

Step-by-step explanation:

From the given figure it is easily noticed that the function is increasing in nature for x<0 and the function is constant in nature for x>0 because the value of y remains unchanged for any value of x, where
`x\geq0`.

The value of function is 3 at x=0.

The value of the function is always 3 for all
`x\geq0`. So,

`f(x)=3` for
`x\geq0`.

The function is a straight line with intercepts (-3,0) and (0,3).

The equation of line is,

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

`y-0=(3-0)/(0-(-3)) (x-(-3))`

`y=(3)/(3) (x+3)`

`y=(x+3)`

For x<0, the function is,

`f(x)=x+3`

Therefore the piecewise function can be defined as,

`f(x)=\begin{cases}x+3 & \text{ if } x<0 \\3& \text{ if } x\geq0\end{cases}`

Therefore option 2 is correct.