Questions: Finding the Domain and Range of a Graph
Determine the domain and range for the graph below. Write your answer in interval notation and in set builder form using a compound inequality.
Note:To type in the ≤ sign, type <= or use the Math Quill by clicking the yellow arrow.
Domain written in interval notation Domain written in set builder form Use a compound inequality
Range written in interval notation Range written in set builder form Use a compound inequality
y R
Transcript text: Finding the Domain and Range of a Graph
Determine the domain and range for the graph below. Write your answer in interval notation and in set builder form using a compound inequality.
Note:To type in the $\leq$ sign, type <= or use the Math Quill by clicking the yellow arrow.
\begin{tabular}{||c||c||}
\hline Domain written in interval notation & \begin{tabular}{c}
Domain written in set builder form \\
Use a compound inequality
\end{tabular} \\
\hline Range written in interval notation & \begin{tabular}{r}
Range written in set builder form \\
Use a compound inequality
\end{tabular} \\
\hline$\square$ & $\left\{y \left\lvert\, \begin{array}{l}\text { R }\end{array}\right.\right.$ \\
\hline
\end{tabular}
Solution
Solution Steps
Step 1: Find the Domain
The domain of a graph is the set of all possible x-values. In this graph, the x-values span from -4 to 2, where -4 is not included and 2 is included.
Interval notation: (-4, 2]
Set builder notation: {x | -4 < x ≤ 2}
Step 2: Find the Range
The range of a graph is the set of all possible y-values. In this graph, the y-values span from -3 to 5, where -3 is not included and 5 is included.
Interval notation: (-3, 5]
Set builder notation: {y | -3 < y ≤ 5}
Final Answer
Domain: (-4, 2], {x | -4 < x ≤ 2}
Range: (-3, 5], {y | -3 < y ≤ 5}