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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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Find the domain of the function. (Enter your answer using interval notation.) \[ f(x)=\frac{1}{x-1} \] 1. Given the general term \( T_{n}=5 \times 3^{n+1} \), determine an expression for the sum of the first \( n \) terms of the series. The function \( f \) defincd by \( f(x)=\frac{a}{x+p}+q \) has the following properties. - The range of \( f \) is \( y \in R, y \neq 2 \) - The axis of symmetry with a positive gradient is \( y=x+1 \) - The graph of \( f \) passes through \( (0 ;-4) \) 6.1 Write down the valuc of \( q \). 6.2 Calculate the values of \( a \) and \( p \). 6.3 Sketch a neat graph of this function. Your graph must include the intercepts with the axcs and asymptotes if any. The function \( f \) defined by \( f(x)=\frac{a}{x+p}+q \) has the following properties. - The range of \( f \) is \( y \in R, y \neq 2 \) - The axis of symmetry with a positive gradient is \( y=x+1 \) - The graph of \( f \) passes through \( (0 ;-4) \) 6.1 Write down the valuc of \( q \). 6.2 Calculate the values of \( a \) and \( p \). 6.3 Sketch a neat graph of this function. Your graph must include the intercepts with the axcs and asymptotes if any. 2. [-/1 Points] DETAILS MY NOTES SPRECALC8 2.1.001. If \( f(x)=x^{3}+1 \), then give the following. (a) the value of \( f \) at \( x=-1 \) is \( f(\square)=\square \) (b) the value of \( f \) at \( x=3 \) is \( f(\square(-1)=\square \) (c) the net change in the value of \( f \) between \( x=-1 \) and \( x=3 \) is \( f(\square) \) (4) 0,42 Determine the values of \( x \) for which each of the following geometric series converges. \( \begin{array}{ll}\text { (1) } x+2 x^{2}+4 x^{3}+\ldots & \text { (2) } 1-x+x^{2}-\ldots \\ \text { (3) }(x+1)+(x+1)^{2}+(x+1)^{3}+\ldots & \text { (4) } 2(1-x)+2(1-x)^{2}+2(1-x)^{3}+\ldots \\ \text { (5) }(2 x-5)+(2 x-5)^{2}+(2 x-5)^{3}+\ldots & \text { (6) } x(7-2 x)^{4}-x(7-2 x)^{5}+x(7-2 x \\ \text { (7) }(3 x-2)^{3}-(3 x-2)^{4}+(3 x-2)^{5}-\ldots & \text { (8) } \\ (2-4 x)+2(2 x-1)^{2}-2(2 x-1)^{3}+\end{array} \) [-/1 Points] DETAILS MY NOTES SPRECALC8 1.8.038. Solve the nonlinear inequality. Express the solution using interval notation. \[ (x-1)(x+8) \geq 0 \] 2 Points] DETAILS MY NOTES SPRECALC8 1.8.092. Recognize the type of inequality and solve the inequality by an appropriate method. Express the answer using interval notation. \( \frac{20}{x-1}-\frac{20}{x} \geq 1 \) (a) Calculate the sum of each of the following geometric series: \( \begin{array}{lll}\text { (1) } 3+12+48+\ldots \text { (to } 10 \text { terms) } & \text { (2) } 4-8+16-\ldots \text { (to } 15 \text { terms) } \\ \text { (3) } 200+100+50+\ldots(\text { to } 8 \text { terms) } & \text { (4) }-27+9-3+\ldots \text { (to } 10 \text { terms) } \\ \text { (5) } x+x^{2}+x^{3}+\ldots \text { (to } 20 \text { terms) } & \text { (6) } x y^{10}+x y^{9}+x y^{8}+\ldots \text { (to } 8 \text { terms) }\end{array} \) Question 2 (2 points) Use the formulas given the Expoenntial Functions packet to determine the following: Suppose you won a contest at the start of 5 th grade that deposited \( \$ 3000 \) in an account that pays \( 5 \% \) interest sompounded quarterly. How much will you have in the account after graduating high school? Express your answer to the nearest dollar. hint: calculate the number of years from the START of 5 th grade to the end high school a \( \$ 3662 \) a \( \$ 4248 \) e \( \$ 139018 \) d \( \$ 4464 \)
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