To find the [tex]$y$[/tex]-intercept of the equation [tex]\( y = 2^{(4x + 3)} - 1 \)[/tex], we need to determine the value of [tex]\( y \)[/tex] when [tex]\( x \)[/tex] is equal to 0.
Given the equation:
[tex]\[ y = 2^{(4x + 3)} - 1 \][/tex]
Step-by-step solution:
1. Substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[ y = 2^{(4 \cdot 0 + 3)} - 1 \][/tex]
2. Simplify inside the exponent:
[tex]\[ y = 2^3 - 1 \][/tex]
3. Calculate the power:
[tex]\[ 2^3 = 8 \][/tex]
4. Subtract 1:
[tex]\[ y = 8 - 1 \][/tex]
[tex]\[ y = 7 \][/tex]
So, the [tex]$y$[/tex]-intercept of the equation [tex]\( y = 2^{(4x + 3)} - 1 \)[/tex] is [tex]\( 7 \)[/tex].
Therefore, on the provided graph, you should place a point at [tex]\((0, 7)\)[/tex]. This is the location of the [tex]$y$[/tex]-intercept.
