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Home Question Bank Math Pre Calculus Archive 2025 January 27

Pre-calculus Questions from Jan 27,2025

Browse the Pre-calculus Q&A Archive for Jan 27,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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In the exponential function \( f(x)=2^{-x}+3 \), what is the end behavior of \( f(x) \) as \( x \) goes to \( \infty \) ? (You can enter pi for positive infinity, ni for negative infinity and dne for does not exist.) In the exponential function \( f(x)=-4^{x} \), what is the end behavior of \( f(x) \) as \( x \) goes to \( \infty \) ? (You can enter pi for positive infinity, ni for negative infinity and dne for does not exist.) In the power function \( f(x)=(-4 x)^{\frac{1}{2}} \), what is the end behavior of \( f(x) \) as \( x \) goes to \( -\infty \) ? (You can enter pi for positive infinity, ni for negative infinity and dne for does not exist.) Homewerk Siven: \( f(x)=-x^{2}+2 x+3 \) and \( g(x)=1-2^{x} \) Sketch the graphs of \( f \) and \( g \) on the same set of axes. Type your answer If \( f(x)=\ln (x) \), what is the transformation that occurs if \( g(x)=\ln (x-5) \) ? (Enter \( s \) for stretch, \( c \) for compress, \( r \) for shift right, I for shift left, \( u \) for shift up, and \( d \) for shift down.) Homework Given: \( f(x)=-x^{2}+2 x+3 \) and \( g(x)=1-2^{x} \) 1.1) Sketch the graphs of \( t \) and \( g \) on the same set of axes. 1.2) For which values of \( x \) is \( f(x) \cdot g(x) \geqslant 0 \) 1.3) Determine the \( y \)-intercept of \( t \) if \( t(x)=-g(x)+1 \) 3. Determine the largest integral value of \( n \) such that \[ \sum_{k=1}^{n} 9\left(\frac{8}{10}\right)^{k-1}<34 \] Given: \( f(x)=-x^{2}+2 x+3 \) and \( g(x)=1-2^{x} \) 1.1) Sketch the graphs of taud \( g \) on the same set of axes. 1.2) For which values of \( x \) is \( f(x)=g(x) \geqslant 0 \) 1.3) Determine the \( y \)-intercept of \( t \) if \( t(x)=-g(x)+1 \) 1.4 The quaph of \( k \) is a reflection of \( g \) abount the \( y \)-axis. White down the equation of \( k \). If \( f(x)=\ln (x) \), what is the transformation that occurs if \( g(x)=\ln (x-5) \) ? (Enter \( s \) for stretch, \( c \) for compress, \( r \) for shift right, I for shift left, \( u \) for shift up, and \( d \) for shift down.) I For the following problem use \( T=2 \pi \sqrt{\frac{L}{g}} \). Let \( \pi \approx 3.14 \) and \( g=32 \) feet per second \( { }^{2} \). A child is swinging on a rope 120 feet long over a river swimming hole. How long does it take (in seconds) to complete one swing back and forth?
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