Question

Graph the exponential function y=0.5(6)x
. Identify the y-intercept.(1 point)
Responses

0.5
0.5

−4
negative 4

1
1

0

Answer 1

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**.