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Home Question Bank Math Pre Calculus Archive 2025 January 21

Pre-calculus Questions from Jan 21,2025

Browse the Pre-calculus Q&A Archive for Jan 21,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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\( f(x)=3 x^{2}+5 \) a. The minimum value is 5 . The domain is all real numbers and the range is \( y \geq 5 \). The function is decreasing to the left of \( x=0 \) and increasing to the right of \( x=0 \). b. The maximum value is 5 . The domain is all real numbers and the range is \( y \leq 5 \). The function is increasing to the left of \( x=0 \) and decreasing to the right of \( x=0 \). c. The minimum value is -5 . The domain is all real numbers and the range is \( y \geq-5 \). T function is decreasing to the left of \( x=0 \) and increasing to the right of \( x=0 \). d. The maximum value is -5 . The domain is all real numbers and the range is \( y \leq-5 \). function is increasing to the left of \( x=0 \) and decreasing to the right of \( x=0 \). Zadanie 12. \( (0-1) \) Do wykresu funkcji \( f \) określonej wzorem \( f(x)=\frac{1}{2}(x-1)^{2}+q \), należy punkt \( A=(-3,5) \). Dokończ zdanie. Wybierz właściwą odpowiedź spośród podanych. Zbiorem wartości funkcji \( f \) jest przedział: \( \begin{array}{llll}\text { A. }\langle 1 ;+\infty) & \text { B. }\langle 5 ;+\infty) & \text { C. }(-\infty ;-3\rangle & \text { D. }\langle-3 ; \infty)\end{array} \) Graph the relationship \( h=10 t-t^{2} \) How much would you have to deposit in an account with a \( 7 \% \) interest rate, compounded monthly, to have \( \$ 1100 \) in your account 10 years later? \[ P=\$[?] \] \[ F=P\left(1+\frac{r}{n}\right)^{n t} \] Round to the nearest cent. Your friend makes a comment about how expensive the baseball card pack was that he purchased. He says 10 years ago he could buy a pack of baseball cards for \( \$ 5 \). Assuming inflation is \( 3 \% \), compounded continuously, how much did he pay for the pack today? Round your answer to the nearest cent (hundredth). 44. What is the inverse of \( f(x)=2^{x}-3 \) ? A. \( f^{-1}(x)=\log _{3}(x+2) \) B. \( f^{-1}(x)=\log _{2}(x+3) \) C. \( f^{-1}(x)=\log _{3}(x-2) \) D. \( f^{-1}(x)=\log _{2}(x-3) \) Cancel Done \( \overleftrightarrow{\Delta B} \) RESET (a) Section 3.6 \#42 Use the Guidelines for Graphing Rational Functions to list out the seven characteristics of the graph. You do not need to graph the function. Cancel Done \( \overleftrightarrow{\Delta B} \) RESET (a) Section 3.6 \#42 Use the Guidelines for Graphing Rational Functions to list out the seven characteristics of the graph. You do not need to graph the function. 1. \( f(x)=2 x+3 \) intervalo \( -3 \leq x \leq 3 \) 2. \( f(x)=x^{2}-2 x \) intervalo \( -3 \leq x \leq 3 \) 3. \( f(x)=3 x-x^{2} \) intervalo \( -3 \leq x \leq 3 \) 4. \( f(x)=4-3 x \) intervalo \( -3 \leq x \leq 3 \) 5. \( f(x)=\frac{x+2}{x} \) intervalo \( -3.5 \leq x \leq 3.5 \) escala 0.5 6. \( f(x)=x^{3} \) intervalo \( -3 \leq x \leq 3 \) 4 of 5 Analyze the graphs and describe the shift that occurs from \( g(x)=5 \sqrt{x+3}-4 \) to \( g(x)=5 \sqrt{x+7}-4 \). For the first response, enter 1 for left and 2 for right. (1 point) The transformation is a shift \( \square \) by \( \square \) units. Check answer Remaining Attempts : 3
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