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Describe the end behavior of the following functions using proper limit notation. (Do not use calculator) !
a) 𝑓 𝑥 = !!! − 7 b) 𝑔 𝑥 = −𝑥 ! + 7𝑥 ! − 4𝑥 + 3 2)
State the roots and their multiplicities of the following function: 𝑓 𝑥 = 𝑥 + 2 𝑥 − 3 ! 𝑥 + 1 ! !! ! !!"
3) Given 𝑓 𝑥 = !! ! !!"!!!" ,evaluate each of the following limits. a) lim!→! 𝑓(𝑥) b) lim!→! 𝑓(𝑥) c) lim!→! 𝑓(𝑥) d) lim!→!! 𝑓(𝑥) 4) Rewrite the following using positive integers. !
a) 3𝑥 ! !
b) ! 𝑥 !! 5) What happens once in a minute, twice in a moment and never in a thousand years? 1)
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Divide. (2𝑥 ! − 3𝑥 ! + 9𝑥 ! − 14𝑥 + 7) ÷ (𝑥 ! + 4) Divide. Then determine if the divisor is a factor of the dividend. Explain your reasoning. (𝑥 ! − 4𝑥 ! + 8𝑥 − 8) ÷ (𝑥 − 2) Write a polynomial function with the following characteristics: Degree: 2 Zeros at −3. Find all zeros of 𝑓 𝑥 = 2𝑥 ! + 5𝑥 − 3. Why is the day after Thanksgiving called “Black Friday”? 1) Solve the following using a sign chart. !!!
< 0 2) Find all zeros of 𝑔 𝑥 = 𝑥 ! + 5. 3) Write the equation of the line secant to 𝑓 𝑥 = −2𝑥 ! + 3𝑥 − 2 on [−2, 2]. 4) Describe the end behavior of the following functions using proper limit notation. a) 𝑓 𝑥 = 4 𝑥 b) 𝑔 𝑥 = 4𝑥 ! 5) When is the first day of Winter? !!! !!!
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Solve the following using a sign chart. 𝑓 𝑥 = 𝑥 ! + 4 𝑥 + 3 ! . Write a polynomial function with the following characteristics: Degree: 4 Zeros at: −2 (𝑤𝑖𝑡ℎ 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑐𝑖𝑡𝑦 𝑜𝑓 2) 4 (with multiplicity of 2) Rewrite the following expressions using a single rational number. !
a) 2 𝑥 4)
b) !
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Describe the end behavior of the following functions using the proper limit statements. a) b) 5) Who won Dancing with the Stars this season? 1)
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Divide. (6𝑥 ! − 8𝑥 ! − 𝑥 ! − 1) ÷ (3𝑥 ! − 4𝑥 + 1) ! ! !!!!"
Determine where 𝑓 𝑥 = !! ! !!"! is zero, undefined, positive, and negative. Express your answers using a sign chart. Rewrite the following using positive integers. !
a) 4𝑥 ! 4)
b) 2𝑥 !! Rewrite the following expressions using a single rational number. !!
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a) − ! 𝑥 ! b) ! 5) Which Peanuts comic strip character carries around a blue blanket? ! ! !! ! !!"!
1) Given 𝑓 𝑥 = ! ! !!!!! , find: a) Domain b) x-­‐intercept(s) (as ordered pairs) c) y-­‐intercept d) removable discontinuities (as ordered pair) (as ordered pairs) e) Vertical Asymptotes (include behavior on each side) f) End Behavior g) Sketch graph using calculator. Include important features found above. TURN OVER !"! !
2) Given 𝑓 𝑥 = !"! ! !!, find: a) Domain b) x-­‐intercept(s) (as ordered pairs) c) y-­‐intercept d) removable discontinuities (as ordered pair) (as ordered pairs) e) Vertical Asymptotes (include behavior on each side) f) End Behavior g) Sketch graph using calculator. Include important features found above.