To find the [tex]\(y\)[/tex]-intercept of the function [tex]\(y = 6^x\)[/tex], you need to determine the value of [tex]\(y\)[/tex] when [tex]\(x = 0\)[/tex]. The [tex]\(y\)[/tex]-intercept is the point where the graph of the function crosses the [tex]\(y\)[/tex]-axis. This happens when the input ([tex]\(x\)[/tex]) is zero.
Here is the step-by-step process:
1. Start with the function:
[tex]\[
y = 6^x
\][/tex]
2. Set [tex]\(x = 0\)[/tex]:
[tex]\[
y = 6^0
\][/tex]
3. Evaluate the expression [tex]\(6^0\)[/tex]:
[tex]\[
6^0 = 1
\][/tex]
When [tex]\(x = 0\)[/tex], [tex]\(y\)[/tex] equals 1.
Therefore, the [tex]\(y\)[/tex]-intercept of the function [tex]\(y = 6^x\)[/tex] is [tex]\((0, 1)\)[/tex]. The correct answer to the given question is 1.
