Question
Determine the horizontal asymptote of the function \[ f(x)=(3) \cdot 10^{x}-5 \]
Ask by Frank Franklin. in Indonesia
Feb 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The function \( f(x) = 3 \cdot 10^{x} - 5 \) does not have a horizontal asymptote.
Solution
Find the horizontal asymptotes of the function \( f(x)=(3) \cdot 10^{x}-5 \).
Function by following steps:
- step0: Find the horizontal asymptotes:
\(f\left(x\right)=3\times 10^{x}-5\)
- step1: Find the horizontal asymptotes:
\(\textrm{No horizontal asymptotes}\)
The function \( f(x) = (3) \cdot 10^{x} - 5 \) does not have a horizontal asymptote.
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Beyond the Answer
To determine the horizontal asymptote of the function \( f(x) = 3 \cdot 10^x - 5 \), we need to analyze the behavior of \( f(x) \) as \( x \) approaches positive and negative infinity. As \( x \) approaches positive infinity, \( 10^x \) grows without bound, and hence \( f(x) \) also goes to positive infinity: \[ \lim_{x \to +\infty} f(x) = +\infty. \] For \( x \) approaching negative infinity, \( 10^x \) approaches zero: \[ \lim_{x \to -\infty} f(x) = 3 \cdot 10^{-x} - 5 = 0 - 5 = -5. \] Thus, the horizontal asymptote is: \[ y = -5. \]
