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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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1. \( f(x)=\frac{3}{x-2} \) Find each of the following functions. \( f(x)=\sqrt{4-x}, g(x)=\sqrt{x^{2}-9} \) (a) \( f+g \) State the domain of the function. (Enter your answer using interval notation.) (b) \( f-g \) State the domain of the function. (Enter your answer using interval notation.) (c) \( f g \) \( \square \) Question 3 (1 point) Which function results when the graph of the function \( y=8^{x} \) is reflected in the \( x \)-axis and stretched vertically by a factor of 3 ? A) \( y=(8)^{-3 x} \) B) \( y=-3(8)^{-x} \) C) \( y=-3(8)^{x} \) D) \( y=3(8)^{-x} \) For the exponential function \( y=2^{x+3}-1 \), which properties does the graph of the function have? A) domain \( \{x \in \mathbb{R}\} \), range \( \{y \in \mathbb{R}\} \), asymptote at \( y=-1 \) B) domain \( \{x \in \mathbb{R}, x>-1\} \), range \( (j \in \mathbb{R}\} \), asymptote at \( y=-1 \) C) domain \( \{x \in \mathbb{R}\} \), range \( \{y \in \mathbb{R}, y \geq-1\} \), asymptote at \( y=1 \) D) domain \( (x \in \mathbb{R}) \), range \( \{y \in \mathbb{R}, y>-1\} \), asymptote at \( y=-1 \) QLESTION 2 Given \( f(x)=2.3^{x}-1 \) and \( g(x)=\frac{4}{x+3} \) A! Write down the equation of the asymptote of \( f \). Find an explicit formula for \( f^{-1} \), Use this formula to graph \( f^{-1}, f \), and the line \( y=x \) on the same screen. To check your work, see whether the graphs of \( f \) and \( f-1 \) are reflections about the line. \[ f(x)=\sqrt{5 x+2} \] \( f^{-1}(x)=\square \) Find a formula for the inverse of the function. \[ f(x)=e^{8 x-7} \] \( f^{-1}(x)=\square \) At the time of her grandson's birth, a grandmother deposits \( \$ 14,000 \) in an account that pays \( 4.5 \% \) compounded monthly. What will be the value of the account at the child's twenty-first birthday, assuming that no other deposits or withdrawals are made during this period? i. Click the icon to view some finance formulas. The value of the account will be \( \$ \square \). (Round to the nearest dollar as needed.) 1. plot \( f(x)=|x-1| \) and determine if a) is \( f(x) \) one to one? \( x(n+t) \) b) is surjective? \( x(n+t) \) c) is mlonotonic? Graph \( y=f(x) \), where \( f(x)=\log _{2}(x-1)+3 \) on the set of axes below.
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