Finding Domain and Range from Graphs Practice

1. What is the domain of ‍$h$?

   
   

   Choose 1 answer:

   1. $-5 \leq x \leq 7$
   2. The $x$-values ‍$-5$, $-2$, $6$ and $7$
   3. $-2 \leq x \leq 6$

   4. The $x$-values ‍$-2$, $-1$, $1$, $5$ and $6$

2. What is the domain of ‍$f$?

   
   

   Choose 1 answer:

   1. $-9 \leq f(x) \leq 9$
   2. $-8 \leq f(x) \leq -4$
   3. $-9 \leq f(x) \leq -2$

   4. $-2 \leq f(x) \leq 9$

3. What is the domain of ‍$g$?

   
   

   Choose 1 answer:

   1. $-7 \leq x \leq 4$
   2. $-4 \leq x \leq 8$
   3. The $x$-values ‍$-4$, $-3$, $0$, $2$ and $8$

   4. The $x$-values ‍$-7$, $-4$, $0$, $3$ and $4$

4. What is the domain of ‍$h$?

   
   

   Choose 1 answer:

   1. $-4 \leq h(x) \leq 6$
   2. The $h$-values ‍$-5$, $-4$, $0$, $2$ and $4$
   3. The $x$-values ‍$-4$, $-2$, $2$, $4$ and $6$
   4. $-5 \leq h(x) \leq 4$

Source: Khan Academy, https://www.khanacademy.org/math/college-algebra/xa5dd2923c88e7aa8:functions/xa5dd2923c88e7aa8:domain-and-range-of-a-function/e/domain_and_range_0.5
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1. The domain of a function is the set of all inputs for which the function is defined.
   

   According to the graph, ‍$h$ is defined for certain points only. So the domain is the list of the input ‍$x$-values where ‍$h$ is defined (or where there are points on the graph). This means the domain of ‍$h$ is the ‍$x$-values ‍$-2$, $-1$, $1$, $5$ and $6$.

   
   

   In conclusion, the domain of the function is the $x$-values ‍$-2$, $-1$, $1$, $5$ and $6$.

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2. The range of a function is the set of all the possible function outputs.

   According to the graph, the largest number that is an output of $f$ is ‍-2, and the smallest number is ‍-9. Every number between them is also an output of ‍$f$ for some input. Therefore, the range of ‍$f$ is $-9 \leq f(x) \leq -2$.

   
   

   In conclusion, the range of the function is $-9 \leq f(x) \leq -2$.
   

   ---

3. The domain of a function is the set of all inputs for which the function is defined.
   

   According to the graph, ‍$h$ is defined for certain points only. So the domain is the list of the input ‍$x$-values where ‍$h$ is defined (or where there are points on the graph). This means the domain of ‍$h$ is the ‍$x$-values ‍$-2$, $-1$, $1$, $5$ and $6$.
   

   
   

   In conclusion, the domain of the function is the $-7 \leq x \leq 4$.

   ---

4. The range of a function is the set of all the possible function outputs.

   According to the graph, ‍$h$ is defined for certain points only. So the range is the list of the output $h(x)$-values where ‍$h$ is defined (or where there are points on the graph). This means the domain of ‍$h$ is the ‍$h(x)$-values ‍$-4$, $-2$, $2$, $4$ and $6$.

   
   

   In conclusion, the range of the function is $h(x)$-values ‍$-4$, $-2$, $2$, $4$ and $6$.