To determine the value of [tex]\( y \)[/tex] for the given point [tex]\((-3, y)\)[/tex] on the graph of [tex]\( y = 3^{-x} \)[/tex], we need to substitute [tex]\( x = -3 \)[/tex] into the equation and solve for [tex]\( y \)[/tex].
Here are the steps to find the value of [tex]\( y \)[/tex]:
1. Start with the given equation:
[tex]\[ y = 3^{-x} \][/tex]
2. Substitute [tex]\( x = -3 \)[/tex] into the equation:
[tex]\[ y = 3^{-(-3)} \][/tex]
3. Simplify the exponent [tex]\(-(-3)\)[/tex]:
[tex]\[ y = 3^3 \][/tex]
4. Calculate [tex]\( 3^3 \)[/tex]:
[tex]\[ y = 27 \][/tex]
Thus, the value of [tex]\( y \)[/tex] when [tex]\( x = -3 \)[/tex] is [tex]\( 27 \)[/tex]. Therefore, the point [tex]\((-3, y)\)[/tex] on the graph of [tex]\( y = 3^{-x} \)[/tex] is [tex]\((-3, 27)\)[/tex].
So, [tex]\( y = 27 \)[/tex].
