Rational Functions & Their Graphs

MAT 111 – Spring 2020 Name ___________________________________________ Quiz 4.1/4.2 – Rational Functions & Their Graphs Identify any vertical and/or horizontal asymptotes. If one does not exist, write DNE. Circle/Box final answer. Label each answer. You MUST show work to support your answer to receive full credit (i.e. factor polynomials, identify how you determined horizontal asymptote, etc.)

1. 𝑓 𝑥 = 𝑥 3

3𝑥+2

2. 𝑔 𝑥 = 𝑥 2−4

𝑥2+2𝑥−8

3. 𝑓 𝑥 = 𝑥−3

𝑥2−16

4.. Identify any vertical or horizontal asymptotes. If one does not exist, write DNE.

Vertical Asymptote(s): Horizontal Asymptotes(s): Identify the interval over which the function is Increasing, decreasing or constant.

#5 & 6 Find the domain/range, vertical/horizontal asymptotes, the x- and y-intercepts, and at least 3 additional points on the graph. If a value does not exist, label it as DNE. Graph the function. Be neat! Label all answers. Show work when possible to receive full credit.

5. 𝑓 𝑥 = −2𝑥+9 𝑥−3

6. 𝑔 𝑥 = 𝑥+1

𝑥2−4

I PROMISE I AM COMPLETING THIS QUIZ ON MY OWN AND I WILL NOT SHARE THE CONTENTS OF THIS QUIZ OR MY ANSWERS WITH ANYONE.

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