Question

Write the equation of the piecewise function ƒ that is represented by its graph.

Answer 1

Answer:

$\left \{ {{f(x)=2;\text{ For }0\leq x1}} \right.$

Step-by-step explanation:

We have been given graph of a piece-wise function. We are asked to write the equation for the given piece-wise function.

We can see that for x values greater than or equal to 0 and less than 1, the function is a line.

We can see that our given line is a horizontal line, so it will be in form $y=C$ intersecting y-axis at $(0,C)$.

The given crosses y-axis at (0,2), therefore, its equation would be $y=2$.

We can see that for x values greater than 1, the graph is a reflected and shifted square root function.

The square root function is reflected across x-axis and has a vertex at (1,1), therefore, our function for second part would be $y=-\sqrt{x-1}+1$.

The function is not defined at $x=1$ and it can a jump continuity.

Therefore, our required piece-wise function would be:

$\left \{ {{f(x)=2;\text{ For }0\leq x1}} \right.$