Question

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

1
1

−4
negative 4

0.5
0.5

0
0

Answer 1

To identify the y-intercept of the exponential function \( y = 0.5(6)^x \), we can evaluate the function when \( x = 0 \).

Substituting \( x = 0 \):

\[
y = 0.5(6)^0 = 0.5(1) = 0.5
\]

So the y-intercept is \( 0.5 \).

### Graphing the Function

1. When \( x = 0 \), \( y = 0.5 \) (y-intercept).
2. As \( x \) increases, \( y \) will increase because the base of the exponential (6) is greater than 1.
3. As \( x \) decreases (becomes negative), the function approaches 0, but never actually reaches it (as \( (6)^x \) approaches 0).

### Conclusion

The y-intercept of the function \( y = 0.5(6)^x \) is:

**0.5**

So the correct response is \( 0.5 \).