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.

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,

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

$y-0=\frac{3-0}{0-(-3)} (x-(-3))$

$y=\frac{3}{3} (x+3)$

$y=(x+3)$

For x<0, the function is,

$f(x)=x+3$

Therefore the piecewise function can be defined as,

$f(x)=\begin{cases}x+3 & \text{ if } x$

Therefore option 2 is correct.