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Home Question Bank Math Pre Calculus Archive 2025 January 02

Pre-calculus Questions from Jan 02,2025

Browse the Pre-calculus Q&A Archive for Jan 02,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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1. The domain of the function \( f(x)=\frac{\ln \sqrt{x-1}}{x^{2}+1} \) is \( \begin{array}{llll}\text { A) }(-1,2) & \text { B) }(0,1) & \text { C) }(1,+\infty) & \text { D) }[-1,1]\end{array} \) \( \begin{array}{ll}1.2 & \text { If } f(x)=\frac{\sqrt{x+2}}{3-3 x^{2}} \text {, for which values of } x \text { is } \\ 1.2 .2 & f(x) \text { non real. } \\ 1.2 .3 & f(x) \text { undefined } \\ 1.2 .4 & f(x)>0\end{array} \) If \( f(x)=\frac{\sqrt{x+2}}{3-3 x^{2}} \), for which values of \( x \) is 1.2.2 \( \quad f(x) \) non real. Liam is using sequences to compare the growth rates of \( h(x)=1.2 x \) and \( j(x)=1.2^{x} \). Which statement correctly describes how Liam should do this and what he will observe? (1 point) Liam should look at where one sequence has terms greater than the terms in the other sequence. The growth rate of \( j(x)=1.2^{x} \) is only greater than the growth rate of \( h(x)=1.2 x \) when its terms are greater. Liam should compare the rates of change of the terms in both sequences. The growth rate of \( h(x)=1.2 x \) will quickly surpass the growth rate of \( j(x)=1.2^{x} \). Liam should compare the rates of change of the terms in both sequences. The growth rate of \( j(x)=1.2^{x} \) will quickly surpass the growth rate of \( h(x)=1.2 x \). Liam should look at where one sequence has terms greater than the terms in the other sequence. The growth rate of \( h(x)=1.2 x \) is greater than the growth rate of \( j(x)=1.2^{x} \) when its terms are greater. The number of people with the flu during an epidemic is a function, \( f \), of the number of days, \( d \), since the apidemic began The equation \( f(d)=40 \). \( \left(\frac{5}{4}\right)^{d} \) defines \( f \). 1. How many people had the flu at the beginning of the epidemic? 2. Each day, the number of infected people grows by a factor of does \( f(1) \) mean in this situation? 4. Does \( f(3.5) \) make sense in this situation? The number of people with the flu during an epidemic is a function, \( f \), of the number of days, \( d \), since the apidemic bega The equation \( f(d)=40 \cdot\left(\frac{5}{4}\right)^{d} \) defines \( f \) 1. How many people had the flu at the beginning of the epidemic? 2. Each day, the number of infected people grows by a factor of 3. What does \( f(1) \) mean in this situation? \( f(3.5) \) make sense in this situation? (114) Determina los puntos de discontinuidad de estas funciones. \( \begin{array}{ll}\text { a) } f(x)=\sqrt{x^{2}+3 x+2} & \text { c) } f(x)=\sqrt{x^{2}+x-2} \\ \text { b) } f(x)=\ln \left(x^{2}+x-6\right) & \text { d) } f(x)=\log \left(x^{2}+4 x-5\right)\end{array} \) For the following function, find \( f(2.1) \) and \( f(4) \). \( f(x)=\left\{\begin{array}{ll}2 x-3, & 0<x \leq 2 \\ \frac{1}{2} x^{2}, & 2<x<4 \\ \log _{2} x, & 4 \leq x<8\end{array}\right. \) (1 point) \( f(2.1)=2.205 \) and \( f(4)=2 \) \( f(2.1)=1.2 \) and \( f(4)=2 \) \( f(2.1)=2.205 \) and \( f(4)=16 \) \( f(2.1)=1.2 \) and \( f(4)=8 \) Check answer Remaining Attempts : 3 To convert the polar equation \( r=4 \) to ectangular form, we use the relationship oetween polar and rectangular coordinates: 9. a) i) Define step function ii) The function is defined as \[ f(x)=\left\{\begin{array}{rr}-4 & \text { if } x<-2 \\ 2 \text { if }-2 \leq x \leq 3 \\ 5 & \text { if } x \geq 3\end{array}\right. \] Draw the graph of \( f(x) \) and state its domain and range, find \( f(-100) \), \( f\left(\frac{1}{2}\right) \). and \( f(203) \). b) Verify that \( x+4 \) is not a factor of the polynomial function \[ f(x)=x^{3}-9 x^{2}+10 x-24 . \] e) Sketch the graph of the function \( f(x) \) and hence state its domain and range. \( f(x)=\left\{\begin{array}{r}x^{2}+1 \text { for } x>1 \\ |x| \text { for }-2 \leq x \leq 1 \\ x+2 \text { for } x 2\end{array}\right. \)
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