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Home Question Bank Math Pre Calculus Archive 2025 January 22

Pre-calculus Questions from Jan 22,2025

Browse the Pre-calculus Q&A Archive for Jan 22,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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For \( f(x)=x^{2}+4 \) and \( g(x)=x^{2}-8 \), find the following functions. a. \( (f \circ g)(x) ; \) b. \( (g \circ f)(x) ; \quad \) c. \( (f \circ g)(3) ; \quad \) d. \( (g \circ f)(3) \) a. \( (f \circ g)(x)=\square \) \( ( \) Simplify your answer.) Assume that \( (\mathrm{a}, \mathrm{b}) \) is a point on the graph of f . What is the corresponding point on the graph of the following function? \( f(x-20) \) What is the point on the graph of \( f(x-20) \) that corresponds to the point \( (\mathrm{a}, \mathrm{b}) \) on the graph of \( f \) ? \( \square \) (Type an ordered pair.) (1 point) Suppose \( f \) is a function of the form \[ f(x)=a^{b x} \] for some constants \( a \) and \( b \). The doubling time for \( f \) is 3 , i.e., \[ f(x+3)=2 f(x) \] for all \( x \) Then \( f(x)=\square \) Matilda wishes to retire at age 67 with \( \$ 1,700,000 \) in her retirement account. When she turns 28 , she decides to begin depositing money into an account with an ApR of \( 9 \% \) compounded monthly. What is the monthly deposit that Matilda must make in order to reach her goal? Round your answer to the nearest cent. if necessary. Formulas omplete the sentence below. uppose that the graph of a function \( f \) is known. Then the graph of \( y=f(x-2) \) may be obtained by a __ shift of the graph of \( f \) ___ anits. Suppose that the graph of a function \( f \) is known. Then the graph of \( y=f(x-2) \) may be obtained by a 2 shift of the graph of \( f \) a distance of 2 units. Let \( f \) be the exponential function defined by \[ f(x)=10^{-(x-3)} \] and determine the following information based on \( f \). (i) Horizontal Asymptote: (ii) Range: (iii) \( y \)-intercept: Let \( f \) be the exponential function defined by \[ f(x)=10^{-(x-3)} \] and determine the following information based on \( f \). (i) Horizontal Asymptote: (ii) Range: (iii) \( y \)-intercept: (iv) Letter Corresponding to Graph: Finding the Domain of a Function In Exercises 21 and 22 , find the domain of the function. \( \begin{array}{ll}\text { 21. } f(x)=\sqrt{25-x^{2}} & \text { 22. } h(x)=\frac{x}{x^{2}-x-6}\end{array} \) Finding the Domain of a Function In Exercises 21 and 22 , find the domain of the function. \( \begin{array}{ll}\text { 21. } f(x)=\sqrt{25-x^{2}} & \text { 22. } h(x)=\frac{x}{x^{2}-x-6}\end{array} \) Determine whether the function is even, odd, or neither. Then determine whether the function's graph is symmetric with respect to the \( y \)-axis, the origin, or neither. \( f(x)=x \sqrt{1-x^{2}} \) Determine whether the fưhcction is even, odd, or neither. Choose the correct answer below. odd even neither
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