Consider the function given by 𝑓 ( 𝑥 ) = 2 𝑥 + 3 3 𝑥 + 1 . What is the range of 𝑓 ? Hint: It may help to find 𝑓 − 1 first.单项选择题

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Question textA glass of lemonade is observed over time through photos and the number of bubbles is noted by taking photographs of the glass every two hours. The number of bubbles added over time diminishes, which means the rate of increase of cumulative bubbles diminishes as well.A saturation-growth model is fitted to the data, where y is the cumulative total number of bubbles and t is time in hours: [math: y(t) = 1351t(t+7.75)]To two decimal places, when does the cumulative total of observed bubbles reach 1248? Answer 1 Question 1[input] hoursCheck Question 1

Question textGuidelines to answer the following question:Fill in the blanks with the correct answers. Do NOT use any spaces or brackets. For all numerical answers, give EXACT values (i.e. do not round your answers) unless instructed otherwise in the question. If using fractions, give answers as SIMPLIFIED fractions using the forward slash (e.g. 1/2 or 5/4). Use - for any negatives. _____________________________________________________________ This question is worth 1+ 3 + 2 + 3 + 1 = 10 marks.For a person with sensitive skin, the amount of time [math: t] (in minutes) the person can be exposed to the sun with minimal burning can be modelled by: [math: S=0.56t+36.7t+1], [math: 0≤t≤15], where [math: S] is the sun strength reading. a) What is the sun strength reading after 1 minute?Answer: Answer 1 Question 6[input] units [1 mark]b) After how many minutes is the sun strength reading predicted to be half its initial value?The initial reading is [math: S=] Answer 2 Question 6[input] unitsTherefore, for the sun strength reading to be half its initial value, this means [math: S=] Answer 3 Question 6[input].This happens after Answer 4 Question 6[input] minutes (rounded to 2 decimal places) [3 marks] c) [math: S] can be rewritten in the form [math: S=at−h+k], where [math: h=] Answer 5 Question 6[input] and [math: k=] Answer 6 Question 6[input]. [2 marks]d) The graph of [math: S] has a Answer 7 Question 6[select: , horizontal, vertical] asymptote with equation Answer 8 Question 6[select: , t=0.56, S=0.56, t=36.7, S=36.7] Its [math: S−] intercept is at [math: (0,] Answer 9 Question 6[input] [math: )].(You may want to sketch the graph of [math: S] on your calculator to help you answer this question. )  [3 marks]e) When will the sun strength reading reach 0 units? Answer: Answer 10 Question 6[select: , After 1 minute, After 2 minutes, After 10 minutes, Never] .  [1 mark]

A possible equation for the graph shown (x > 0) is:

A possible equation for the graph shown (x > 0) is:

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