Chapter 4.7, Problem 57HP

To determine

To write:The piecewise function of the given graph.

Answer to Problem 57HP

The piecewise function of the given graph is

  $y=\left\{\begin{array}{l}-\left(x-6\right)\text{ if }x<6\\ 0\text{ if }x<6\\ \left(x-6\right)\text{ if }x>6\end{array}\right\}$ .

Explanation of Solution

Given:

The given graph is

  

Calculation:

To write the absolute value function for the graph, observe the given graph. It can be seen that the graph is shifted towards right by the units 6. The upward shift of the graph is zero that means k =0.

From the graph it can be observed that

1. The value of function comes out to be a straight line if x < 6. This line approaches towards the left.
2. The graph shows the value 6 for x and the value of function is zero at x = 6.
3. The value of function comes out to be a straight line if x > 6. This line approaches towards the right.

Therefore, the function for the graph is:

  $y=\left\{\begin{array}{l}-\left(x-6\right)\text{ if }x<6\\ 0\text{ if }x=6\\ \left(x-6\right)\text{ if }x>6\end{array}\right\}$ .