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Home Question Bank Math Pre Calculus Archive 2024 November 25

Pre-calculus Questions from Nov 25,2024

Browse the Pre-calculus Q&A Archive for Nov 25,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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A patient ingests 5 grams of a certain drug which dissolves away at a constant rate of \( 10 \% \) per hour. How long will it take before there is only one gram left? Determine each feature of the graph of the given function. \[ f(x)=\frac{-5}{2 x-7} \] Determine each feature of the graph of the given function. \[ f(x)=\frac{x^{2}-3 x}{2 x^{2}+8 x} \] Determine each feature of the graph of the given function. \[ f(x)=\frac{x^{2}-3 x}{2 x^{2}+8 x} \] Answer Attempt 1 out of 2 Horizontal Asymptote: \( y=\square \) Vertical Asymptote: \( x=\square \)-Intercept: \( (\square, 0) \) \( y \)-Intercept: \( (0, \square) \) For each function, state the vertex and whether the function has a maximum or minimum value. Explain how you decided. \( \begin{array}{ll}\text { a) } f(x)=2(x-3)^{2}-5 & \text { c) } f(x)=-(x+1)^{2}+6 \\ \text { b) } f(x)=-3(x-5)^{2}-1 & \text { d) } f(x)=(x+5)^{2}-3\end{array} \) Determine each feature of the graph of the given function. \[ f(x)=\frac{3 x+9}{x^{2}-9} \] Answer Attempt 1 out of 2 Horizontal Asymptote: \( y=\square \) Nortical Asymptote: \( x=\square \) No horizontal asymptote \( x \)-Intercept: \( y \)-Intercept: \( (0, \square) \) No vertical asymptote Hole: \( (\square, \square \)-intercerept Identify the maximum or minimum value and the domain and range of the graph of the function \( y=2(x+2)^{2}-3 \). a. maximum value: -3 domain: all real numbers \( \leq-3 \) range: all real numbers b. minimum value: -3 domain: all real numbers range: all real numbers \( \geq-3 \) maximum value: 3 domain: all real numbers range: all real numbers \( \leq 3 \) d. minimum value: 3 domain: all real-numbers \( \geq 3 \) range: all real numbers The graph of the rational function \( f(x)=\frac{x-2}{x^{2}+4 x-5} \) will have a vertical asymptote at The graph of which of the following rational functions will have an oblique asymptote? a.) \( f(x)=\frac{5 x^{3}+2 x^{2}-8}{2 x^{2}+6 x-1} \) b.) \( f(x)=\frac{x-1}{2 x-4} \) c.) \( f(x)=\frac{5 x^{5}-2 x^{3}+x+1}{7 x^{8}-2 x^{5}+3 x-7} \) d.) \( f(x)=\frac{3 x^{2}-1}{4 x^{4}+2 x+2} \) ( Determine each feature of the graph of the given function. \[ f(x)=\frac{3 x+9}{x^{2}-9} \]
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