To determine the range of the given relation [tex]\( R_1 \)[/tex] where [tex]\( y = 4x + 1 \)[/tex] and the domain is [tex]\(\{0, 1, 2\}\)[/tex], follow these steps:
1. Substitute each value of the domain into the equation to find the corresponding value of [tex]\( y \)[/tex]:
- For [tex]\( x = 0 \)[/tex]:
[tex]\[
y = 4(0) + 1 = 0 + 1 = 1
\][/tex]
- For [tex]\( x = 1 \)[/tex]:
[tex]\[
y = 4(1) + 1 = 4 + 1 = 5
\][/tex]
- For [tex]\( x = 2 \)[/tex]:
[tex]\[
y = 4(2) + 1 = 8 + 1 = 9
\][/tex]
2. List the corresponding [tex]\( y \)[/tex]-values obtained from the calculations:
[tex]\[
\{1, 5, 9\}
\][/tex]
Thus, the range of the relation [tex]\( R_1 = \{(x, y): y = 4x + 1\} \)[/tex] with the given domain [tex]\(\{0, 1, 2\}\)[/tex] is [tex]\(\{1, 5, 9\}\)[/tex].
