6. For the function: f(x) = 글, f"(x) = , f"(x) = x-2 2(x-6) a. Find domain and range. b. Determine the equations of the vertical and horizontal asymptotes. Describe the behavior of the function on either side of the vertical asymptote. Show your calculations. c. Find all the intercepts.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
Problem 15T
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6. For the function:
f(x) = , f'(x) = , f"(x) = 2(x-6)
x4
a. Find domain and range.
b. Determine the equations of the vertical and horizontal asymptotes. Describe the
behavior of the function on either side of the vertical asymptote. Show your
calculations.
c. Find all the intercepts.
d. Find all critical points (determine if they are local max./min./neither) and determine
the intervals of increase and decrease.
e. Determine the intervals of concavity and points of inflections.
f. Sketch and label: intercepts, asymptotes, critical point(s), point of inflection.
Transcribed Image Text:6. For the function: f(x) = , f'(x) = , f"(x) = 2(x-6) x4 a. Find domain and range. b. Determine the equations of the vertical and horizontal asymptotes. Describe the behavior of the function on either side of the vertical asymptote. Show your calculations. c. Find all the intercepts. d. Find all critical points (determine if they are local max./min./neither) and determine the intervals of increase and decrease. e. Determine the intervals of concavity and points of inflections. f. Sketch and label: intercepts, asymptotes, critical point(s), point of inflection.
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