Draw the Graph of the Function \(f(x)\)
Question
The function \(f\) is defined by
\[ f(x)= \begin{cases} 1-x, & x<0 \\ 1, & x=0 \\ x+1, & x>0 \end{cases} \]Draw the graph of \(f(x)\).
Solution
The function is defined in three parts.
Case 1: \(x<0\)
\[ f(x)=1-x \]This is a straight line with slope \(-1\).
Some points on this line are:
\[ (-1,2),\ (-2,3) \]Since \(x<0\), the point at \(x=0\) is not included.
Therefore, draw an open circle at
\[ (0,1) \]Case 2: \(x=0\)
\[ f(0)=1 \]Plot the point
\[ (0,1) \]as a solid point.
Case 3: \(x>0\)
\[ f(x)=x+1 \]This is a straight line with slope \(1\).
Some points on this line are:
\[ (1,2),\ (2,3) \]Since \(x>0\), the point at \(x=0\) is not included.
Therefore, draw an open circle at
\[ (0,1) \]Graph Description
The graph consists of two straight lines meeting at the point \((0,1)\).
- For \(x<0\), draw the line \(y=1-x\).
- For \(x>0\), draw the line \(y=x+1\).
- At \(x=0\), place a solid point at \((0,1)\).
The graph forms a V-shape symmetric about the y-axis.
Final Answer
The graph of the function consists of:
- \(y=1-x\) for \(x<0\)
- \(y=x+1\) for \(x>0\)
- A solid point at \((0,1)\)