For each rational function, find (a) y-intercept point, (b) the roots, and (c) the equation of the vertical asymptote, and (d) equation of the horizontal asymptote. Then, use this information to graph the rational function. The image presents the following mathematical function: \[ f(x) = \frac{3x - 6}{x + 2} \]Below the function, there is a blank coordinate grid provided for graphing. The grid consists of evenly spaced horizontal and vertical lines, forming squares, which can be used to plot points and graph the function. This setup is typically used in educational contexts to help students visualize and analyze rational functions. The function can be explored to understand concepts such as asymptotes, intercepts, and behavior as $ x $ approaches certain values.

a) The given function fx=3x-6x+2 For y-intercept, put x=0 y=0-60+2=-3 point (0, -3)

Answered: For each rational function, find (a)…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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For each rational function, find (a) y-intercept point, (b) the roots, and (c) the equation of the vertical asymptote, and (d) equation of the horizontal asymptote. Then, use this information to graph the rational function.

The image presents the following mathematical function:

\[ f(x) = \frac{3x - 6}{x + 2} \]

Below the function, there is a blank coordinate grid provided for graphing. The grid consists of evenly spaced horizontal and vertical lines, forming squares, which can be used to plot points and graph the function.

This setup is typically used in educational contexts to help students visualize and analyze rational functions. The function can be explored to understand concepts such as asymptotes, intercepts, and behavior as $ x $ approaches certain values.

Expert Solution

Step 1

a) The given function

$f (x) = \frac{3 x - 6}{x + 2}$

For y-intercept, put x=0

y= $\frac{0 - 6}{0 + 2} = - 3$

point (0, -3)

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