Tutors Answer Your Questions about Functions (FREE)
Question 1182274: At this one coastal city, the tides vary greatly during the day. During May, the predicted height of the tides are 2.5 m at 4 AM, 17 m at 10 AM, 2.5 m at 4 PM and 17 m at 10 PM. Assume we start the graph at midnight. What is the height of the tide at 11 AM? Round to the nearest tenth.
Click here to see answer by greenestamps(13195)  |
Question 1182215: At this one coastal city, the tides vary greatly during the day. During May, the predicted height of the tides are 2.5 m at 4 AM, 17 m at 10 AM, 2.5 m at 4 PM and 17 m at 10 PM. Assume we start the graph at midnight. What is the height of the tide at 11 AM? Round to the nearest tenth.
Click here to see answer by greenestamps(13195)  |
Question 1182537: Kendra is having her breakfast on a balcony, 20m high when she accidentally knocks down a flower pot. A man, 10m away, is innocently walking along the street at a constant velocity of 4 m/s when the pot fell. Will the innocent man be hit by the pot or will he miraculously be able to avoid the impending accident? The man is 1.7m tall. Explain and prove your answer.
Click here to see answer by math_tutor2020(3816) |
Question 1182943: (a) The functions 𝑓 and 𝑔 are defined as follows.
𝑓(𝑥) = 3𝑥*2 where 𝑥 ∈ (−1, 1) and 𝑔(𝑥) = 𝑥 + 2, where 𝑥 ∈ (−1, 1).
i) Find 𝑅(𝑓) and 𝑅(𝑔).
ii) Draw the graphs of 𝑓 and 𝑔.
iii) Find 𝑓 ∘ 𝑔 and 𝑔 ∘ 𝑓.
iv) Show that 𝑓(𝑥) is not one to one function.
(b) The function ℎ is defined as ℎ(𝑥) = 3𝑥*2 where 𝑥 ∈ (−∞, 0].
i) Show that ℎ is a one to one function.
ii) Find the inverse function h-1 of ℎ.
iii) Show that,
(α) ℎ-1 ∘ ℎ(𝑥) = 𝑥, where 𝑥 ∈ (−∞, 0].
(β) ℎ ∘ ℎ−1(𝑥) = 𝑥, where 𝑥 ∈ [0, ∞).
(γ) Are the functions ℎ−1∘ ℎ and ℎ ∘ ℎ−1
the same? Explain your
answer.
Click here to see answer by ikleyn(52750)  |
Question 1182916: A relation ⋆ is defined on z by x ⋆ y if and only if there exists k ϵ z such that y=x+5k .
Is ⋆ reflexive?
Is ⋆ symmetric?
Is ⋆ anti-symmetric?
Is ⋆ transitive?
Is ⋆ an equivalence relation, a partial order, both, or neither?
Thanks in advance!
Click here to see answer by ikleyn(52750)  |
Question 1183376: hello! I am completing a table and I just wanted to make sure I was doing this correctly!
𝑔(𝑥)=ln(𝑥−3)
x g(x)
4 0 I used the equations g(x)=ln(4-3)
6 1.099 g(x)=ln(6-3)
8 1.61 g(x)=ln(8-3)
10 1.95 g(x)=ln(10-3)
12 2.197 g(x)=ln(12-3)
Click here to see answer by MathLover1(20849)  |
Question 1183370: f(x) = x4 − 12x3 + 37x2 − 12x + 36
(a) Find all zeros of the function. (Enter your answers as a comma-separated list.)
x = I found this to be i,-i,6
(b) Write the polynomial as a product of linear factors.
f(x) =
(c) Use your factorization to determine the x-intercepts of the graph of the function. Use a graphing utility to verify that the real zeros are the only x-intercepts. (Enter your answers as a comma-separated list. If no x-intercepts exist, enter DNE.)
x =
Click here to see answer by Solver92311(821)  |
Question 1183371: f(x) = 25x3 − 80x2 − 74x − 24
(a) Use a graphing utility to find the real zeros of the function. (Enter your answers as a comma-separated list.)
x =
(b) Use the real zeros to find the exact values of the imaginary zeros. (Enter your answers as a comma-separated list.)
x =
Click here to see answer by Solver92311(821)  |
Question 1183390: given set Z(26) = {0,1,2,3,...25}
Let a and b be integers. Consider the function f: Z(26) -> Z(26) defined by f(x) = ax + b (mod 26).
a)Prove that f(x) = 3x + b is bijective for any b.
b) find all the values of a for which the function f is bijective.
Click here to see answer by ikleyn(52750)  |
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Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205, 11206..11250, 11251..11295, 11296..11340, 11341..11385, 11386..11430, 11431..11475, 11476..11520, 11521..11565, 11566..11610, 11611..11655, 11656..11700, 11701..11745, 11746..11790, 11791..11835, 11836..11880, 11881..11925, 11926..11970, 11971..12015, 12016..12060, 12061..12105, 12106..12150, 12151..12195, 12196..12240, 12241..12285, 12286..12330, 12331..12375, 12376..12420, 12421..12465, 12466..12510, 12511..12555, 12556..12600, 12601..12645, 12646..12690, 12691..12735, 12736..12780, 12781..12825, 12826..12870, 12871..12915, 12916..12960, 12961..13005, 13006..13050, 13051..13095, 13096..13140, 13141..13185, 13186..13230, 13231..13275, 13276..13320, 13321..13365, 13366..13410, 13411..13455, 13456..13500, 13501..13545, 13546..13590, 13591..13635, 13636..13680, 13681..13725, 13726..13770, 13771..13815, 13816..13860, 13861..13905, 13906..13950, 13951..13995, 13996..14040, 14041..14085, 14086..14130, 14131..14175, 14176..14220, 14221..14265, 14266..14310, 14311..14355, 14356..14400, 14401..14445, 14446..14490, 14491..14535, 14536..14580, 14581..14625, 14626..14670, 14671..14715, 14716..14760, 14761..14805, 14806..14850, 14851..14895, 14896..14940, 14941..14985, 14986..15030, 15031..15075, 15076..15120, 15121..15165, 15166..15210, 15211..15255, 15256..15300, 15301..15345, 15346..15390, 15391..15435, 15436..15480, 15481..15525, 15526..15570, 15571..15615, 15616..15660
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