Question

Which graph represents the piecewise-defined function?

Answer 1

Answer: The correct option is 1.

Explanation:

The given piecewise function is,

$y=\begin{cases}-\frac{4}{5}x-3 & \text{ if } x$

It means if x<0, then

$f(x)=-\frac{4}{5}x-3$

If $x\geq2$, then

$f(x)=3x-10$

Since the f(x) is defined for x<0 and $x\geq2$, therefore the function f(x) is not defined for $0\leq x$.

From the graph 2, 3 and 4 we can easily noticed that for each value of x there exist a unique value of y, therefore the function is defined for all values of x, which is not true according to the given piecewise function.

Only in figure the value of y not exist when x lies between 0 to 2, including 0. It means the function is not defined for $0\leq x$, hence the first option is correct.