Question

do not write on this paper!!domain and range worksheetname: _____________ date______ periodstate the domain and range for each graph and then state if the graph is a function (write yes or no).finally, state whether the graph is discrete or continuous. write out the word.1) domain_______range_______function?_______2) domain_______range_______function?_______3) domain_______range_______function?_______4) domain_______range_______function?_______5) domain_______range_______function?_______6) domain_______range_______function?_______7) domain_______range_______function?_______8) domain_______range_______function?_______9) domain_______range_______function?_______10) domain_______range_______function?_______11) domain_______range_______function?_______12) domain_______range_______function?_________

Explanation:

Step1: Analyze mapping 1

Domain: $\{0, 3, 4, 5, 9\}$; Range: $\{0, 1, 2, 4, 6\}$; Each domain value has one range value, so it is a function.

Step2: Analyze graph 2

Domain: $\{-4, -2, 0, 2, 3, 4\}$; Range: $\{-2, -1, 0, 2, 3\}$; Passes vertical line test, so it is a function.

Step3: Analyze graph 3

Domain: All real numbers, $\mathbb{R}$; Range: $\{y \mid y \geq -4\}$; Passes vertical line test, so it is a function.

Step4: Analyze graph 4

Domain: All real numbers, $\mathbb{R}$; Range: $\{y=1\}$; Passes vertical line test, so it is a function.

Step5: Analyze graph 5

Domain: $\{-2, 0, 2, 4\}$; Range: $\{-3, -1, 1, 3\}$; Passes vertical line test, so it is a function.

Step6: Analyze graph 6

Domain: $\{x \mid x \leq 4\}$; Range: $\{y \mid y \leq 3\}$; Passes vertical line test, so it is a function.

Step7: Analyze graph 7

Domain: All real numbers, $\mathbb{R}$; Range: $\{y \mid y \geq 2\}$; Passes vertical line test, so it is a function.

Step8: Analyze mapping 8

Domain: $\{3, 4, 5, 6, 9\}$; Range: $\{3, 4, 5, 8, 9\}$; Domain value 5 maps to 2 range values, so it is not a function.

Step9: Analyze graph 9

Domain: $\{-4, -2, 0, 2, 4\}$; Range: $\{-4, -2, 0, 2, 4\}$; Fails vertical line test (x=0 has 3 y-values), so it is not a function.

Step10: Analyze graph 10

Domain: All real numbers, $\mathbb{R}$; Range: $\{y \mid y \geq -3\}$; Passes vertical line test, so it is a function.

Step11: Analyze graph 11

Domain: $\{-3, -1, 1, 3\}$; Range: $\{-4, -2, 0, 2\}$; Passes vertical line test, so it is a function.

Step12: Analyze graph 12

Domain: $\{-3, -1, 1, 3\}$; Range: $\{-3, -1, 1, 3\}$; Fails vertical line test (x=1 has 3 y-values), so it is not a function.

Answer:

1. Domain: $\{0, 3, 4, 5, 9\}$; Range: $\{0, 1, 2, 4, 6\}$; Function? Yes
2. Domain: $\{-4, -2, 0, 2, 3, 4\}$; Range: $\{-2, -1, 0, 2, 3\}$; Function? Yes
3. Domain: $\mathbb{R}$; Range: $\{y \mid y \geq -4\}$; Function? Yes
4. Domain: $\mathbb{R}$; Range: $\{y=1\}$; Function? Yes
5. Domain: $\{-2, 0, 2, 4\}$; Range: $\{-3, -1, 1, 3\}$; Function? Yes
6. Domain: $\{x \mid x \leq 4\}$; Range: $\{y \mid y \leq 3\}$; Function? Yes
7. Domain: $\mathbb{R}$; Range: $\{y \mid y \geq 2\}$; Function? Yes
8. Domain: $\{3, 4, 5, 6, 9\}$; Range: $\{3, 4, 5, 8, 9\}$; Function? No
9. Domain: $\{-4, -2, 0, 2, 4\}$; Range: $\{-4, -2, 0, 2, 4\}$; Function? No
10. Domain: $\mathbb{R}$; Range: $\{y \mid y \geq -3\}$; Function? Yes
11. Domain: $\{-3, -1, 1, 3\}$; Range: $\{-4, -2, 0, 2\}$; Function? Yes
12. Domain: $\{-3, -1, 1, 3\}$; Range: $\{-3, -1, 1, 3\}$; Function? No