Answer :

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.