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Home Question Bank Math Pre Calculus Archive 2025 January 07

Pre-calculus Questions from Jan 07,2025

Browse the Pre-calculus Q&A Archive for Jan 07,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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If \( f(x)=\frac{x^{2}}{x-1} \) then find the value of \( f(\sec \theta) \) 3. Sketch the graph of each of the following: (4 marks). \( \begin{array}{ll}\text { a. } y=\log _{4} x & \text { c. } y=\log _{0} \cdot 25 x \\ \text { b. } y=2 \log _{3} x & \text { d. } y=\log _{5} x^{3}\end{array} \) \( f(x)=\frac{\sqrt{x+2}}{3-3 x^{2}} \), for which values of \( x \) is \( 2 \quad f(x) \) non real. If the function \( h(x) = \sqrt{x^2 - 9} \), what are the restrictions on its domain? Representa una función exponencial Seleccione una: a. \( f(x)=\log 3 \) b. \( f(x)=5^{x} \) c. \( f(x)=\frac{3}{x^{3}} \) d. \( f(x)=x^{2} \) \( f(x)=\frac{\sqrt{x+2}}{3-3 x^{2}} \), for which values of \( x \) is \( 2.2 \quad f(x) \) non real. \( 2.3 \quad f(x) \) undefined \( 2.4 \quad f(x)>0 \) John identified the order of transformations undergone from \( f(x)=x^{2} \) to \( -(f(3 x+1)+2) \) as the following: Step \#1: horizontal compression Step \#2: horizontal translation to the left Step \#3: vertical translation up Step \#4: horizontal reflection In which step did John make a mistake? 5 Determinaţi intervalele de monotonie ale funcţilor: \( \begin{array}{ll}\text { a) } f(x)=\log _{2}(5 x-1) ; & \text { b) } f(x)=\log _{\frac{1}{2}}(-2 x+8) ; \\ \text { c) } f(x)=\log _{0,2}(x-5) ; & \text { d) } f(x)=\log _{3}\left(x^{2}-4\right)\end{array} \) c. \( f(x)=\log _{6}|x-3| \) \( |x-3|>0 \) oursnon In's Nathan owns a model airplane that he decides to sell to Liam. The mode girplane costs Nathan \( \$ 60 \), and he plans to sell it for \( \$ 150 \). Between Natha house and Liam's house is a 6 -mile-wide river. Liam's house is located 28 miles downstream on the opposite side of the river. To deliver the model airplane, Nathan must cross the river using a boat and then drive the remaining distance in a car. The boat charges \( \$ 0.6 \) per mile and travels at a speed of 12 miles per hour. The car charges \( \$ 1.2 \) per mile and travels at a speed of 25 miles per hour. Liam requires Nathan to deliver the airplane by 7.00 p.m., and for every hour Nathan is late, Liam will reduce the payment by \$5. Nathan begins his journey at \( 4: 30 \) p.m. How many miles should Nathan travel by boat to maximize his profit? Round to the nearest whole number
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