Test your knowledge: domain and range from graph questions.

📚 Quick Study Guide

• 🔍 The domain of a function is the set of all possible input values (x-values) for which the function is defined. Look at the graph from left to right.
• 📈 The range of a function is the set of all possible output values (y-values) that the function can produce. Look at the graph from bottom to top.
• ♾️ Use interval notation to express the domain and range. For example, $[a, b]$ means including $a$ and $b$, while $(a, b)$ means excluding $a$ and $b$. Use $\infty$ and $-\infty$ for unbounded intervals.
• 🛑 Pay attention to open and closed circles on the graph. Open circles indicate that the point is not included, while closed circles indicate that the point is included.
• 📉 If the graph extends indefinitely in a direction, the domain or range will include infinity.

🧪 Practice Quiz

1. What is the domain of the function represented by the following graph (assume the graph extends infinitely to the left and right)?
   1. $(-\infty, \infty)$
   2. $[0, \infty)$
   3. $(-\infty, 0]$
   4. $[0, 5]$
2. What is the range of the function represented by the following graph (assume the graph extends infinitely upwards)?
   1. $[2, \infty)$
   2. $(-\infty, \infty)$
   3. $(-\infty, 2]$
   4. $[0, 2]$
3. Given the graph of a line segment from point (1, 3) to (5, 7) inclusive, what is the domain?
   1. $[3, 7]$
   2. $[1, 5]$
   3. $(1, 5)$
   4. $(3, 7)$
4. Given the graph of a parabola opening downwards with a vertex at (2, 4), what is the range?
   1. $[4, \infty)$
   2. $(-\infty, 4]$
   3. $(-\infty, \infty)$
   4. $[0, 4]$
5. What is the domain of a function whose graph is a single point at (3, 5)?
   1. ${3}$
   2. ${5}$
   3. $(-\infty, \infty)$
   4. ${(3, 5)}$
6. What is the range of a function whose graph is a vertical line at x = 2?
   1. ${2}$
   2. $(-\infty, \infty)$
   3. $[2, \infty)$
   4. Cannot be determined
7. Consider a graph with a hole at (4, 2). What is true about the range?
   1. The range includes 2.
   2. The range excludes 4.
   3. The range excludes 2.
   4. The range is all real numbers.