Graphing Piecewise-Defined Functions Practice

1. $f(x) = \begin{cases}\dfrac{1}{2}x+6 & , &  -4\le x < 0\\\\-5 & , & 0 \le x\le 7\end{cases}$

   What is the graph of ‍$f$?

   Choose 1 answer:

   1. 
   2. 

   
   

2. $f(x) = \begin{cases}5-\dfrac{1}{3}x & , &  -9\le x < -3\\\\\dfrac{2}{3}x & , & -3 \le x \le 8\end{cases}$

   What is the graph of ‍$f$?

   Choose 1 answer:

   1. 
   2. 

   
   

3. $f(x) = \begin{cases}-\dfrac{2}{3}x & , &  -5\le x\le 2\\\\1 & , & 2< x\le 6\end{cases}$

   What is the graph of ‍$f$?

   Choose 1 answer:

   1. 
   2. 

   
   

4. $h(x) = \begin{cases}2-x & , &  -7\le x \le5\\\\3x-21 & , & 5 < x \le 9\end{cases}$

   What is the graph of ‍$h$?

   Choose 1 answer:

   1. 
   2. 

   
   

Source: Khan Academy, https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:absolute-value-piecewise-functions/x2f8bb11595b61c86:piecewise-functions/e/piecewise-graphs-linear
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1. The options are the same except for the inclusion (or exclusion) of the point at $x=0$.

   According to the formula, ‍$x=0$ should be included in the second case, i.e. the one graphed on ‍$0\le x\le 7$.

   The correct graph is ‍B.

   
   

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2. The options are similar. However, notice that the second case ends at different ‍$x$-values.

   The second case should be graphed on the interval ‍$-3\le x\le 8$.

   The correct graph is ‍A.

   
   

   ---

3. The options are similar. However, notice that the ‍$x$-value where the function changes from the first case to the second is different.

   The ‍$x$-value where the function changes from the first case to the second should be ‍$x=2$.

   The correct graph is ‍B.

   
   

   ---

4. The options are similar. However, the case for ‍$-7\le x \le5$ is different.

   We can see that by noting that the first case in graph A begins at ‍(-7, 8)and the first case in graph ‍B begins at (-7, 9).

   The rule for the first case is ‍$y=2-x$. When ‍$x=-7$, the ‍$y$-value should be ‍9.
   

   The correct graph is ‍B.