Login
Premium
Home Question Bank Math Pre Calculus Archive 2025 January 06

Pre-calculus Questions from Jan 06,2025

Browse the Pre-calculus Q&A Archive for Jan 06,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

error msg
3 Să se determine semnul functiei \( f: \mathbf{R} \rightarrow \mathbf{R}, f(x)=\ln \left(x^{2}-3 x+3\right) \) I. Determine the domain of definition of each of the following expressions: 1) \( A=\sqrt{|x-3|-1} \) 2) \( B=\frac{2+x}{3+|-x|} \) 3) \( C=\frac{2}{-2+|x+5|} \) 4) \( E=\frac{x}{\sqrt{1-|x+2|}} \) QUESTION 4 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: \( \begin{array}{ll}3.1 & \text { Shift two units to the left } \\ 3.2 & \text { Shift } 3 \text { units up } \\ 3.3 & \text { Shift } 1 \text { unit right and } 2 \text { units down } \\ 3.4 & \text { The equation of the new hyperbola has new asymptotes at } x=-4 \text { and } y=-1\end{array} \) If \( f(x)=\frac{\sqrt{x+2}}{3-3 x^{2}} \), for which values of \( x \) is \( f(x) \) non real. 282. Napišite enačbo hiperbole z goriščema \( F_{1}(10,0) \) in \( F_{2}(-10,0) \), točka \( T(12,3 \sqrt{5}) \) pa leži na hiperboli. 11. ให้ \( f=\left\{(x, y) \left\lvert\, y=\frac{3 x+2}{4}\right.\right\} \) ข้อใดคือ \( D_{f^{-1}} \) \( \begin{array}{ll}\text { ก. } R & \text { ข. } R-\left\{\frac{3}{4}\right\} \\ \text { ค. } R-\left\{-\frac{1}{2}\right\} & \text { ง. } R-\left\{\frac{1}{2}\right\}\end{array} \) 4. La taille d'une population de bactéries triple toutes les 4 heures. Combien de temps met-elle pour doubler? \( \begin{array}{lll}\text { A. } 4 \cdot \frac{\ln (3)}{\ln (2)} \text { heures } & \text { C. } 3 \cdot \frac{\ln (4)}{\ln (2)} \text {, heures } & \text { E. Aucune des autres propositions n'est correcte } \\ \text { B. } 4 \cdot \frac{\ln (2)}{\ln (3)} \text { heures } & \text { D. } 3 \cdot \frac{\ln (2)}{\ln (4)} \text { heures } & \text { F. Abstention }\end{array} \) \begin{tabular}{l|ll} ค. \( D_{f} \subset(-2,3) \) & ง. \( D_{f} \subset(0,4) \) \\ 8. ให้ \( r=\left\{(x, y) \left\lvert\, y=\frac{x+1}{x}\right.\right\} \) เรนจ์ของ \( r \) คือข้อใด \\ \( \begin{array}{ll}\text { ก. } R-\{1\} & \text { ข. } R-\{-1,1\} \\ \text { ค. }(-\infty,-1) \cup(1, \infty) & \text { ง. }(-\infty,-1] \cup[1, \infty)\end{array} \)\end{tabular} Show that the maximum value of \( \sqrt{-x^{2}+4 x+12} \) is 4 .
Prev 1 2 Next
1 2
Prev Next
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy