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Home Question Bank Math Pre Calculus Archive 2025 January 29

Pre-calculus Questions from Jan 29,2025

Browse the Pre-calculus Q&A Archive for Jan 29,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Describe the transformations from the parent function \( f(x)=\sqrt{x} \) to \( g(x)=\sqrt{2 x} \) Answer Attempt 1 out of 2 right 2 units horizontal compress by a factor of \( 1 / 2 \) reflection over the \( x \)-axis 2 units Describe the transformations from the parent function \( f(x)=\sqrt{x} \) to \( g(x)=\sqrt{x+2} \) Answer Attempt 1 out of 2 right 2 units horizontal compress by a factor of \( 1 / 2 \) reflection over the x-axis \( f(x)=\frac{1}{x-2}-3 \) CALCOLA L'INIETTIVITAA, SURIETTIVITAA E LA FUNZIONE INVERSA When you calculate (In) 7 , you would be finding the value of which of the following expression \( \log _{10} 7 \) \( \log _{7} e \) \( \log _{7} 10 \) \( \log _{e} 7 \) Question 3. Sketch a graph \( \mathrm{y}=\mathrm{f}(\mathrm{x}) \) of a function defined everywhere on \( (-\infty, \infty) \) with the following properties: a) \( f(-1)=6 \) b) \( \lim _{x \rightarrow-1} f(x)=3 \) c) \( \lim _{x \rightarrow 3^{-}} f(x)=5 \) d) \( \lim _{x \rightarrow 3^{+}} f(x)=2 \) e) \( \lim _{x \rightarrow-\infty} \mathrm{f}(\mathrm{x})=0 \) f) \( \lim _{x \rightarrow \infty} f(x)=\infty \) Write the domain and range of the square root function in interval notation. What is the correct domain and range for the graph of \( y=\frac{1}{2} \sqrt{8-3 x}-2 \) ? (1 point) domain \( \left(-\infty, \frac{8}{3}\right] \); range \( (-2, \infty) \) domain \( \left(-\infty, \frac{8}{3}\right) \); range \( [-2, \infty) \) domain \( \left(-\infty, \frac{8}{3}\right] \); range \( [-2, \infty) \) domain \( \left(-\infty, \frac{8}{3}\right) \); range \( (-2, \infty) \) Write the domain and range of the quadratic function in interval notation. What is the correct domain and range for the graph o \( d(x)=-x^{2}+6 x+2 \) ? (1 point) domain \( (-\infty, \infty) \); range \( (-\infty, 11] \) domain \( (-\infty, 11) \); range \( (-\infty, \infty) \) domain \( (-\infty, \infty) \); range \( (-\infty, 11) \) domain \( (-\infty, \infty) \); range \( (-\infty, 3] \) Which function would cause a horizontal stretch by a factor of 4 on \( q(x)=\sqrt{2(x-1)} \) and its reflection over the line \( x= \) (1 point) \( m(x)=4 \sqrt{-2(x-1)} \) \( h(x)=\sqrt{-\frac{1}{4}(x-1)} \) \( f(x)=\sqrt{\frac{1}{2}(x-1)} \) \( k(x)=\sqrt{-\frac{1}{2}(x-1)} \) ribe the transformations that bring \( g(x)-\sqrt{4 x+1}-3 \) to \( h(x)=-\frac{2}{3} \sqrt{4 x+1}-3 \). (1 point) reflection over the line \( x=-3 \) and a vertical compression by a factor of \( \frac{3}{2} \) reflection over the line \( y \)-axis and a vertical stretch by a factor of \( \frac{3}{2} \) reflection over the line \( x=-3 \) and a vertical compression by a factor of \( \frac{2}{3} \) reflection over the line \( y=-3 \) and a vertical compression by a factor of \( \frac{2}{3} \) Analyze the graphs \( b(x)=\frac{2}{3} \sqrt{x-9}+1 \) and \( k(x)=\frac{2}{3} \sqrt{\frac{10}{7}(x-9)}+1 \), and determine the transformation that is occurring. (1 point) horizontal stretch by a factor of 0.8 horizontal compression by a factor of 0.7 horizontal stretch by a factor of \( \frac{7}{10} \) horizontal compression by a factor of \( \frac{10}{7} \)
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