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Home Question Bank Math Pre Calculus Archive 2025 January 01

Pre-calculus Questions from Jan 01,2025

Browse the Pre-calculus Q&A Archive for Jan 01,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Mathematics Crade 10 NSC Whelyear Examumexion FY QUESTION 4 \( f(x)=-2 x^{2}+2 \) and \( g(x)=2^{x}+1 \) are the defining equations of graphs of \( f \) and \( g \) respectively. 4.1 Write down an equation for the asymptote of \( g \). 4.2 Sketch the graphs of \( f \) and \( g \) on the same set of axes, clearly showing All intercepts with the axes, twaning points and 5 asymptotes. 4.3 Write down the range of \( f \). 4.4 Determine the maximum value of h if \( h(x)=3^{f(x)} \). 4.5 What transformation does the graph of \( y=f(x) \) undergo in orden to obtain graph of \( y=2 x^{2}-2 \) ? Mathematics Grade 10 Question 4 \( f(x)=-2 x^{2}+2 \) and \( g(x)=2^{x}+1 \) are the defining equations of graphs of \( f \) and \( g \) respectively. 4.1 Write down an equation for the asymptote of \( g \). 4.2 Sketch the graphs of \( f \) and \( g \) on the same set of axes, clearly showing All intercepts with the axes, turning points and 2019 asymptotes. 4.3 Write down the range of \( f \). 4.4 Determine the maximum value of \( h \) if \( h(x)=3^{f(x)} \) 4.5 What transformation does the graph of \( y=f(x) \) undergo in order to obtain graph of \( y=2 x^{2}-2 \) ? b) Using Lagrange's formula for interpolation find the value of \( y \) when \( x=2 \) from the ( \( ) \) following table \[ \begin{array}{lrrrr} x: & -2 & -1 & 0 & 4 \\ y: & -2 & 4 & 1 & 8 \end{array} \] Exercises 1. Find these terms of the sequence \( \left\{a_{n}\right\} \), where \( a_{n}=2 \cdot(-3)^{n}+5^{n} \). \( \begin{array}{ll}\text { a) } a_{0} & \text { b) } a_{1} \\ \text { c) } a_{4} & \text { d) } a_{5}\end{array} \) Låt \( f(x)=|x+1|-|x-1| \). a) Lös ekvationen \( f(x)=1 \). What conditions must be true for \( C \) in the equation \( x^{2}+C y^{2}=36 \) for an ellipse to have a vertical major axis? a) \( \ln 300-\ln 9+\ln 5 \) 23. Determine whether each of these functions is a bijection from \( \mathbf{R} \) to \( \mathbf{R} \). a) \( f(x)=2 x+1 \) b) \( f(x)=x^{2}+1 \) c) \( f(x)=x^{3} \) d) \( f(x)=\left(x^{2}+1\right) /\left(x^{2}+2\right) \) QUESTION 4 Sketch on the same set of axes the graphs of \( f(x)=-2 x^{2}-4 x+6 \) and \( g(x)=-2+2^{x-1}+1 \). Clearly indicate all intercepts with the axes, tuming point(s) and asymptote(s). Wenn der Graph von \( f(x) = \sqrt{x} \) um 4 Einheiten nach unten verschoben wird, welche Funktion beschreibt den neuen Graphen?
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