To find the specified range of the function [tex]\( y = 4x^2 + 3x - 1 \)[/tex] for the given domain [tex]\(\{-1, 0, 2\}\)[/tex], follow these steps for each [tex]\( x \)[/tex] value in the domain:
1. Evaluate the function at [tex]\( x = -1 \)[/tex]:
[tex]\[
y = 4(-1)^2 + 3(-1) - 1
\][/tex]
[tex]\[
y = 4 \cdot 1 - 3 - 1
\][/tex]
[tex]\[
y = 4 - 3 - 1
\][/tex]
[tex]\[
y = 0
\][/tex]
So, when [tex]\( x = -1 \)[/tex], [tex]\( y = 0 \)[/tex].
2. Evaluate the function at [tex]\( x = 0 \)[/tex]:
[tex]\[
y = 4(0)^2 + 3(0) - 1
\][/tex]
[tex]\[
y = 0 + 0 - 1
\][/tex]
[tex]\[
y = -1
\][/tex]
So, when [tex]\( x = 0 \)[/tex], [tex]\( y = -1 \)[/tex].
3. Evaluate the function at [tex]\( x = 2 \)[/tex]:
[tex]\[
y = 4(2)^2 + 3(2) - 1
\][/tex]
[tex]\[
y = 4 \cdot 4 + 6 - 1
\][/tex]
[tex]\[
y = 16 + 6 - 1
\][/tex]
[tex]\[
y = 21
\][/tex]
So, when [tex]\( x = 2 \)[/tex], [tex]\( y = 21 \)[/tex].
Therefore, the specified range for the given domain [tex]\(\{-1, 0, 2\}\)[/tex] is:
[tex]\[
\{0, -1, 21\}
\][/tex]
