To determine the value of [tex]\( y \)[/tex] when the point [tex]\( (-1, y) \)[/tex] lies on the graph of the function [tex]\( y = 3^{x+1} \)[/tex], follow these steps:
1. Identify the given function and point:
The function is [tex]\( y = 3^{x+1} \)[/tex] and the point is [tex]\( (-1, y) \)[/tex].
2. Substitute [tex]\( x = -1 \)[/tex] into the function:
[tex]\( y = 3^{x+1} \)[/tex]
When [tex]\( x = -1 \)[/tex]:
[tex]\[
y = 3^{(-1) + 1}
\][/tex]
3. Simplify the exponent:
[tex]\[
y = 3^{0}
\][/tex]
4. Evaluate [tex]\( 3^0 \)[/tex]:
By the properties of exponents, any non-zero number raised to the power of zero is 1.
[tex]\[
3^0 = 1
\][/tex]
Therefore, the value of [tex]\( y \)[/tex] is 1.
Putting all these steps together, when [tex]\( (-1, y) \)[/tex] lies on the graph of [tex]\( y = 3^{x+1} \)[/tex], the value of [tex]\( y \)[/tex] is [tex]\( \boxed{1} \)[/tex].
