Question

name: topic: date: class: main ideas/questions notes/examples relations a set of ordered pairs. can be shown in a _, _, or expressed as an _. the set of x - values is called the _ and the set of y - values is called the _. a relation with distinct points is called _. a relation with connected lines or curves is called _. function a relation in which each element of the domain is paired with exactly one element of the range. function: not a function: this means x - values do not repeat! function: not a function: vertical line test in order to be a function, a vertical line can not pass through more than one point in the relation. directions: find the domain and range of each relation. then, determine if the relation is a function. 1. {(-1, -9), (0, -5), (4, 3), (6, -2)} d = _ r = _ function? _ 2. {(5, 2), (-3, 4), (5, -6), (8, 0)} d = _ r = _ function? _ 3. x y 7 -8 2 3 0 -1 -4 3 d = _ r = _ function? _ 4. x y 10 0 15 3 18 7 24 11 d = _ r = _ function? _

Explanation:

Step1: Recall domain and range definitions

Domain is the set of x - values and range is the set of y - values.

Step2: For relation 1: {(-1, -9), (0, -5), (4, 3), (6, -2)}

Domain \(D=\{-1,0,4,6\}\), range \(R =\{-9,-5,3,-2\}\). Since each x - value is unique, it is a function.

Step3: For relation 2: {(5, 2), (-3, 4), (5, -6), (8, 0)}

Domain \(D=\{-3,5,8\}\), range \(R=\{ - 6,0,2,4\}\). The x - value 5 is repeated, so it is not a function.

Step4: For relation 3: \(

$$\begin{array}{|c|c|}\hline x&y\\\hline7& - 8\\\hline2&3\\\hline0& - 1\\\hline-4&3\\\hline\end{array}$$

\)
Domain \(D=\{-4,0,2,7\}\), range \(R=\{-8,-1,3\}\). Each x - value is unique, so it is a function.

Step5: For relation 4: \(

$$\begin{array}{|c|c|}\hline x&y\\\hline10&0\\\hline15&3\\\hline18&7\\\hline24&11\\\hline\end{array}$$

\)
Domain \(D = \{10,15,18,24\}\), range \(R=\{0,3,7,11\}\). Each x - value is unique, so it is a function.

Answer:

1. \(D=\{-1,0,4,6\}\), \(R =\{-9,-5,3,-2\}\), Function? Yes
2. \(D=\{-3,5,8\}\), \(R=\{ - 6,0,2,4\}\), Function? No
3. \(D=\{-4,0,2,7\}\), \(R=\{-8,-1,3\}\), Function? Yes
4. \(D = \{10,15,18,24\}\), \(R=\{0,3,7,11\}\), Function? Yes