To graph the exponential function \( y = 0.5(6)^x \) and identify the y-intercept, we need to determine the value of \( y \) when \( x = 0 \).
Step 1: Find the y-intercept.
When \( x = 0 \):
\[ y = 0.5(6)^0 \]
Since \( (6)^0 = 1 \):
\[ y = 0.5 \times 1 = 0.5 \]
So, the y-intercept of the function is \( 0.5 \).
Step 2: Graph the function.
The function \( y = 0.5(6)^x \) is an exponential growth function because the base (6) is greater than 1. The graph will rise steeply as \( x \) increases and will approach \( 0 \) as \( x \) decreases toward negative infinity.
Final Response:
The y-intercept of the function \( y = 0.5(6)^x \) is 0.5.