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Home Question Bank Math Pre Calculus Archive 2025 January 12

Pre-calculus Questions from Jan 12,2025

Browse the Pre-calculus Q&A Archive for Jan 12,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Given: \( f(x)=\frac{x+1}{x-1} \) (a) Show that the graph of \( f \) is a hyperbola with a horizontal asymptote of \( y=1 \). (b) Determine the equation of the vertical asymptote. (c) Sketch the graph of \( y=f(x) \). Given: \( f(x)=\frac{x+1}{x-1} \) (a) Show that the graph of \( f \) is a hyperbola with a horizontal asymptote of \( y=1 \). (b) Determine the equation of the vertical asymptote. (c) Sketch the graph of \( y=f(x) \). La forma cartesiana del numero complesso \( w=\left(\frac{1+i \sqrt{3}}{1-i \sqrt{3}}\right)^{10} \) è: QUESTION 3 The equation of a hyperbola is given by \( f(x)=\frac{3}{x-7}-4 \). Write down the equation of the new function that is formed when \( f \) is transformed as follows: 3.1 Shift two units to the left Sketch on the same set of axes the graphs of \( f(x)=-2 x^{2}-4 x+6 \) and \( g(x)=-2 \cdot 2^{x-1}+1 \) Clearly indicate all intercepts with the axes, turning point(s) and asymptote(s). Sketch on the same set of axes the graphs of \( f(x)=-2 x^{2}-4 x+6 \) and \( g(x)=-2 \cdot 2^{x-1}+1 \) Clearly indicate all intercepts with the axes, turning point(s) and asymptote(s). The equation of a hyperbola is given by \( f(x)=\frac{3}{x-7}-4 \). Write down the equation of the new function that is formed when \( f \) is transformed as follows: \( \begin{array}{ll}3.1 & \text { Shift two units to the left } \\ 3.2 & \text { Shift } 3 \text { units up } \\ 3.3 & \text { Shift I unit right and } 2 \text { units down } \\ 3.4 \quad \text { The equation of the new hyperbola has new asymptotes at } x=-4 \text { and } y=-1\end{array} \) 2. Determine the domain of definition for the following functions. \[ \begin{array}{r}f_{1}(x)=\sqrt[4]{x-x^{3}}, \quad f_{2}(x)=\ln (x-3)-\ln (x), \quad f_{3}(x)=\ln \left(1-\frac{3}{x}\right) \\ f_{4}(x)=\ln (1+\lfloor x\rfloor), \quad f_{5}(x)=\ln (\ln (x))\end{array} \] 4. Odredite prinodno podrucje deflnicie funkeife \( f \) \[ \text { b) } f(x)=\sqrt{\frac{2 x-1}{3 x+2}} \] 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.
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