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Home Question Bank Math Pre Calculus Archive 2025 January 23

Pre-calculus Questions from Jan 23,2025

Browse the Pre-calculus Q&A Archive for Jan 23,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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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: \( 3.1 \quad \) Shift two units to the left \( 3.2 \quad \) Shift 3 units up \( 3.3 \quad \) Shift 1 unit right and 2 units down 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). [8] The radioactive substance uranium- 240 has a half-life of 14 hours. The amount \( A(t) \) of a sample of uranium- 240 remaining (in grams) after \( t \) hours is giv the following exponential function. \[ A(t)=2800\left(\frac{1}{2}\right)^{\frac{t}{14}} \] Find the amount of the sample remaining after 9 hours and after 60 hours. Round your answers to the nearest gram as necessary. Amount after 9 hours: grams Determine the end behavior and number of turning points of each polynomial function. \( \begin{array}{l}\text { 3. } f(x)=x^{3}-14 x-4 \\ \text { 4. } g(x)=5-17 x^{7}+9 x^{10}\end{array} \) \begin{tabular}{l} Suppose that the future price \( p(t) \) of a certain item is given by the following exponential function. In this function, \( p(t) \) is measured in dollars and \( t \) is \\ number of years from today. \\ \( p(t)=1200(1.039)^{t} \) \\ Find the initial price of the item. \\ \$1200 \\ \hline \( \begin{array}{l}\text { Does the function represent growth or decay? } \\ \text { Browth o decay }\end{array} \) \\ By what percent does the price change each year? \\ \hline\( \% \)\end{tabular} Emily's parents put \( \$ 1,500 \) in her bank account for college tuition. At an interest rate of \( 8.25 \% \) compounded semiannually, what will be the balance after 18 years? \( \$ 6,273.50 \) \( \$ 6,314.08 \) \( \$ 6,385.72 \) \( \$ 6,427.94 \) Suppose that the dollar value \( v(t) \) of a certain car that is \( t \) years old is given by the following exponential function. \[ \begin{array}{l}v(t)=29,900(0.91)^{t} \\ \text { Find the initial value of the car. } \\ \text { Does the function represent growth or decay? } \\ \text { O growth } \quad \text { O decay } \\ \text { By what percent does the value of the car change each year? } \\ \square \%\end{array} \] \( \begin{array}{l}\text { A psychologist is studying the capacity of the human mind to process information. He has found that the percentage of information one particular } \\ \text { participant can recall after } t \text { months have passed can be modeled by the following logarithmic function. } \\ \text { What percentage of information is retained after } 3 \text { months? Round your answer to the nearest whole percentage, if necessary, } \\ \text { Answer } 2 \text { Points }\end{array} \) Prev Given the function \( h(x)=\frac{2}{x-2}+1 \). 4.2.1 Write down the equations of the asymptotes of \( h \). 4.2.2 Determine the equation of the decreasing axis of symmetry of \( h(x-1) \) (3) 14) An exponential function can be modeled by the function \( P=2(1.45)^{x} \). Which of the following statements is true? Select all that apply. A. \( \square \) This function models exponential growth. B. \( \square \) This function models exponential decay. C. \( \square \) The initial amount is 0.45 . D. \( \square \) The initial amount is 2 . E. \( \square \) The rate is \( 1.45 \% \). F. \( \square \) The rate is \( 45 \% \). 2. Given the graph of \( f(x)=\sqrt{x} \), what happens to the graph when \( f(x) \) is replaced by \( 2 f(-(x+4))-3 \) ?
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