circuit training – the rational function name

Circuit Training – The Rational Function Name _______________________________ Directions: Begin in call #1. Do the work necessary to answer the question. Circle your answer, then search for it and call that cell #2. Proceed in this manner until you complete the circuit. A calculator is not needed to do any of these problems. Answer: −9 # ___1___ Given = !!! !!! , find 3 . Answer: 0 # _______ What is the range of the rational function = ! !!! ? Answer: −4 # _______ For the function = !!! !!! , solve = 2. Answer: − ! ! # _______ What is (are) the xintercept(s) of the function = !!! !!! ? Answer: ! ! # _______ What is the domain of the function = !!!! !!!! ? Answer: ! ! # _______ How many vertical asymptotes does the rational function = !!! ! ! !! have? (if there are no vertical asymptotes, look for 0) Answer: ! ! ! # _______ Given = !! ! !! !!! , find −1 . Answer: 1 # _______ Which − value is not in the domain of = !!!! !! ! !! ? choices: ! ! , !!, ! ! ! Answer: = 5 − 2 # _______ List the equations of the asymptotes for the rational function = !! ! !!!!! ! ! !!!!!" . Answer: = 0, = 5 # _______ List the equations of the vertical and/or horizontal asymptotes for the rational function = ! ! !! !!! . Answer: undefined # _______ What is the yintercept of the function = !!! !!! ? Answer: −∞, 3 ∪ (3, ∞) # _______ What is the equation of the horizontal asymptote to the graph of = ! !!! ? y = _____ © Virge Cornelius 2018 virgecornelius.com

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Page 1: Circuit Training – The Rational Function Name

!!! , find 𝑓 3 .

Answer: 0 # _______ What is the range of the rational function 𝑦 = !

!!!?

Answer: −4 # _______ For the function 𝑓 𝑥 = !!!

!!! , solve

𝑓 𝑥 = 2.

Answer: −!!

# _______ What is (are) the x-‐intercept(s) of the function 𝑓 𝑥 = !!!

!!! ?

Answer: !! # _______ What is the domain of the function 𝑔 𝑥 = !!!!

!!!! ?

Answer: !! # _______ How many vertical asymptotes does the rational function 𝑦 = !!!

!!!! have?

(if there are no vertical asymptotes, look for 0)

Answer: !!!

# _______ Given 𝑔 𝑥 = !!!!!

!!! , find 𝑔 −1 .

Answer: 1 # _______ Which 𝑥 − value is not in the domain of 𝑝 𝑥 = !!!!

!!!!! ?

choices: !!, !!, !

Answer: 𝑦 = 5𝑥 − 2 # _______ List the equations of the asymptotes for the rational function 𝑦 = !!!!!!!!

!!!!!!!" .

Answer: 𝑦 = 0, 𝑥 = 5 # _______ List the equations of the vertical and/or horizontal asymptotes for the rational function 𝑦 = !!!!

!!! .

Answer: undefined # _______ What is the y-‐intercept of the function 𝑓 𝑥 = !!!

!!! ?

Answer: −∞, 3 ∪ (3,∞) # _______ What is the equation of the horizontal asymptote to the graph of 𝑦 = !

!!!?

y = _____

Page 2: Circuit Training – The Rational Function Name

Answer: − !!

# _______ What is the equation of the vertical asymptote for the function 𝑝 𝑥 = !!!!

!!!! ?

x = ______

Answer: −∞, 0 ∪ (0,∞) # _______ How many vertical asymptotes does 𝑦 = !!!

!!!!" have?

(if there are no vertical asymptotes, look for 0)

Answer: (−∞,∞) # _______ The function 𝑦 = !!!

!!! is not defined for

which 𝑥 −value(s) ? choices: !!, !, !

Answer: there are none # _______ The rational function 𝑓 𝑥 = !"!

!!!!!!!!

has a “slant” or “oblique” asymptote. What is its equation?

Answer: 2 # _______ How many vertical asymptotes does the function 𝑦 = !

!!!! have?

(if there are no vertical asymptotes, look for 0)

Answer: (3,∞) # _______ Solve 𝑓 𝑥 = 0 given 𝑓 𝑥 = !"!!

!!!!.

Answer: ! !! # _______ List the equations of the vertical and/or horizontal asymptotes for the rational function 𝑦 = !!!

!!!!" .

Answer: 5 # _______ Determine ℎ(3) for ℎ 𝑥 = !!!

!!!! .

Answer: −3 # _______ As the value of 𝑥 get very large (i.e. approaches ∞) for the function 𝑦 = !"!!!!

!!!!, what value does 𝑦

approach?

Answer: 𝑥 = 5,𝑦 = 2 # _______ What is the domain of 𝑦 = !

!!!! ?

Answer: !! # _______ What is the equation of the horizontal asymptote for the function 𝑝 𝑥 = !!!!

!!!! ?

y = ______

Answer: 3 # _______ What is the domain of 𝑦 = !

!!! ?

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