Question
Rewrite the function \( g(x)=\frac{4 x-6}{x} \) in the form \( g(x)=\frac{a}{x-h}+k \) \( g(x)=\frac{\square}{\square}+\square \)
Ask by King Hodgson. in the United States
Feb 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( g(x) = 4 - \frac{6}{x} \)
Solution
Calculate or simplify the expression \( \frac{4x-6}{x} \).
Divide the polynomials by following steps:
- step0: Using Long Division to Divide Polynomials:
\(\frac{4x-6}{x}\)
- step1: Calculate:
\(4+\frac{-6}{x}\)
The function \( g(x) = \frac{4x-6}{x} \) can be rewritten in the form \( g(x) = \frac{a}{x-h} + k \) as \( g(x) = 4 + \frac{-6}{x} \).
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution The Deep Dive
To rewrite the function \( g(x)=\frac{4 x-6}{x} \) in the desired form, we start by simplifying it. We can split the fraction: \[ g(x) = \frac{4x}{x} - \frac{6}{x} = 4 - \frac{6}{x} \] Now, this can be expressed as: \[ g(x) = -\frac{6}{x} + 4 \] Thus, we can identify \( a = -6 \), \( h = 0 \), and \( k = 4 \). So, in the desired format, we get: \[ g(x) = \frac{-6}{x - 0} + 4 \] This gives us the final result: \[ g(x) = \frac{-6}{x} + 4 \] Therefore, filling in the blanks: \( g(x)=\frac{-6}{x} + 4 \)
