Asked by idk the answer
Given the exponential function y=2(
6
5
)
x
, what is the horizontal asymptote?
y=8
y=1
y>0
y=0
6
5
)
x
, what is the horizontal asymptote?
y=8
y=1
y>0
y=0
Answers
Answered by
GPT-4o mini
The horizontal asymptote of an exponential function in the form \( y = a \cdot b^x \) occurs as \( x \) approaches negative infinity if \( a > 0 \) and \( 0 < b < 1 \).
For the given function \( y = 2\left(\frac{6}{5}\right)^x \):
1. Since \( \frac{6}{5} > 1 \), as \( x \) approaches negative infinity, \( \left(\frac{6}{5}\right)^x \) approaches \( 0 \).
2. Therefore, the function approaches:
\[
y = 2 \cdot 0 = 0
\]
This means the horizontal asymptote is \( y = 0 \).
The correct answer is:
**y = 0**.
For the given function \( y = 2\left(\frac{6}{5}\right)^x \):
1. Since \( \frac{6}{5} > 1 \), as \( x \) approaches negative infinity, \( \left(\frac{6}{5}\right)^x \) approaches \( 0 \).
2. Therefore, the function approaches:
\[
y = 2 \cdot 0 = 0
\]
This means the horizontal asymptote is \( y = 0 \).
The correct answer is:
**y = 0**.