Chapter 3.7, Problem 45PFA

To determine

To find the function of the given graph.

Answer to Problem 45PFA

  $f(x)=\{\begin{array}{l}x+1,\text{ if }x<2\\ x+2,\text{ if }x\ge 3\end{array}$

Explanation of Solution

Given:

  

Assume that each box is 1 unit.

Looking closely at the graph, the given graph represents a piecewise function.

Here, the points that intersect are given clearly are $(1,2)$ and $(1,3)$

Also, in the graph one of the points is dark and the other is not. So, the one that is dark is included and the other is not included.

So, the values of x at dark circle is included, so $x\ge 3$ and the point is $(1,3).$

When the value of $x=1$ , the value of y is 2. When we add 1 to x the value of y is 2. So, one of the piece function is $x+2$ when $x\ge 3.$

Similarly, the values of x which is not a dark circleis not included, so $x<2$ and the point is $(1,2).$

When the value of $x=1$ , the value of y is 3. When we add 2 to x the value of y is 3. So, one of the piece function is $x+1$ when $x<2.$

Hence, the piece functions are combined and is represented as $f(x)=\{\begin{array}{l}x+1,\text{ if }x<2\\ x+2,\text{ if }x\ge 3\end{array}.$

Conclusion:

Therefore, the function is $f(x)=\{\begin{array}{l}x+1,\text{ if }x<2\\ x+2,\text{ if }x\ge 3\end{array}.$