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Home Question Bank Math Pre Calculus Archive 2024 November 15

Pre-calculus Questions from Nov 15,2024

Browse the Pre-calculus Q&A Archive for Nov 15,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Evaluate or simplify the expression without using a calculator. \( e^{\ln 3 x^{3}} \) \( e^{\ln 3 x^{3}}=\square \) Evaluate or simplify the expression without using a calculator. \( e^{\ln 146} \) 27 Multiple Choice 1 point Solve the problem. The population of an animal species in a certain area is modeled by \( \mathbf{F}(\mathrm{t})=400 \mathrm{log}(2 t+3) \) where \( t \) is the time in months since the species was introduced to the area. Find the population of this species in the area 6 months after the species is introduced. 74 704 240 6. Graph \( y=\log _{\frac{1}{2}}(x)+ \) 2. Analyze the function where \( 0<b<1 \). Domain: Range: \( \lim _{x \rightarrow 0^{+}} f(x) \) Find the vertical and horizontal asymptotes for \( g(x)=\frac{\sqrt{x^{2}-4}}{2-x} \) Hence, determine a general formula for the pattern \( 0 ;-6 ;-20 ;-42 \ldots \) Simplify your answer as far as possible. ESTION 4 c) \( =-2 x^{2}+2 \) and \( g(x)=2^{x}+1 \) are the defining equations of graphs \( f \) and \( g \) respectively. Write down an equation for the asymptote of \( g \). Sketch the graphs of \( f \) and \( g \) on the same set of axes, clearly showing ALL intercepts with the axes, turning points and asymptotes. Write down the range of \( f \). Determine the maximum value of \( h \) if \( h(x)=3 /(x) \). What transformation does the graph of \( y=f(x) \) undergo in order to obtain the 11 A ball is dropped from a height of 10 feet. The ball repeatedly bounces, and the maximum height of the ball after each bounce is \( 20 \% \) less than the previous maximum height. Which of the following arguments is correct regarding a sequence that can be used to model the successive maximum heights, in feet? 2 Encontrar el dominio de la función \( A(x)=\frac{\sqrt{\frac{x}{x-1}}}{|x|-\left|\frac{3}{2} x+5\right|} \) 1. Transform the following equations to canonical forms a) \( x^{2}+4 x y+4 y^{2}-20 x+10 y-50=0 \) b) \( 3 x^{2}+10 x y+3 y^{2}-12 x-12 y+4=0 \) c) \( x^{2}+2 x y+y^{2}-4 x-4 y+3=0 \) d) \( 9 x^{2}+24 x y+16 y^{2}-126 x+82 y-59=0 \) e) \( 3 x^{2}-8 x y-3 y^{2}+10 x-13 y+8=0 \) f) \( 3 x^{2}-5 x y+6 y^{2}+11 x-17 y+13=0 \) g) \( 9 x^{2}+24 x y+16 y^{2}+34 x+62 y+47=0 \) h) \( x^{2}-4 x y+4 y^{2}-12 x-6 y-39=0 \) Realice la gráfica de la siguiente función: \( g(x)=\log _{5}(x-6) \) Luego indique: a) Dominio y el rango de la función. b) Ecuación de la asíntota. c) Intercepto con los ejes.
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