To find the value of [tex]\( y \)[/tex] for the given point [tex]\((3, y)\)[/tex] on the graph of [tex]\( y = -\left(2^x\right) \)[/tex], we will follow these steps:
1. Start with the equation of the graph: [tex]\( y = -\left(2^x\right) \)[/tex].
2. Substitute the [tex]\( x \)[/tex]-coordinate of the given point, [tex]\( x = 3 \)[/tex], into the equation.
3. Calculate [tex]\( 2^3 \)[/tex], which equals 8.
4. Apply the negative sign as indicated in the equation.
Thus:
[tex]\[ y = -\left(2^3\right) \][/tex]
[tex]\[ y = -8 \][/tex]
Therefore, the value of [tex]\( y \)[/tex] is [tex]\(-8\)[/tex].
Among the options given:
- [tex]\(-8\)[/tex]
- [tex]\(-6\)[/tex]
- [tex]\(\frac{1}{8}\)[/tex]
The correct value of [tex]\( y \)[/tex] is [tex]\(-8\)[/tex].
