Pre-calculus Questions from Nov 12,2024

Browse the Pre-calculus Q&A Archive for Nov 12,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. \[ y=2400(1.78)^{x} \] Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. \[ y=28(1.01)^{x} \] 1) Esboce o gráfico de cada função a seguir: a) \( f(x)=4 x-3 \) b) \( f(x)=-2 x \) c) \( g(x)=x^{2}-10 x+21 \) d) \( g(x)=-2 x^{2}+4 x-2 \) e) \( h(x)=\left\{\begin{array}{c}x^{2}, \text { se } x<0 \\ x, \text { se } 0 \leq x \leq 1 \\ 1, \text { se } x>1\end{array}\right. \) f) \( h(x)=\left\{\begin{array}{r}-x^{2}+3, \text { se } x>2 \\ 3, \text { se } x \leq 2\end{array}\right. \) QUESTION SIX MARKS A company industrial printer was purchased for \( K 18000 \) on 1 st January. On 1 st January each following year, the value of the industrial printer is, \( 80 \% \) of its value on 1 st January in the previous year. a. Geometrically calculate for the value of the industrial printer exactly 6 years after it was purchased? a. \( a_{n}=1+(-1) n \quad n \leq 4 \) b. \( a_{n}=\sqrt[3]{n} 3<n<5 \) c. \( a_{n}=\frac{n}{(-1)^{11}} \) d. \( a_{n}=2^{n}-3 n \quad n \geq 1 \) 5.- \( f(x)=\sqrt{x-2} \) 6. \( -y=\frac{2}{\sqrt{x}} \) Determina cuáles de las siguientes funciones so inyectivas. Para las funciones que no sean inyectiva encuentra un ejemplo que muestre esta situación. 60. \( f(x)=-2 x^{3}-1 \) 3520 Ange för varje funktion skärningspunkten med \( y \)-axeln med hur många procent \( y \)-värdet förändras när \( x \) ökar med 1 . \( \begin{array}{ll}\text { a) } f(x)=30 \cdot 1,35^{x} & \text { c) } f(x)=2^{x} \\ \text { b) } f(x)=10000 \cdot 0,7^{x} & \text { d) } f(x)=0,967^{x}\end{array} \) 11 Let \( c \in \mathbb{R} \), If \( a=i-3 j+c k \) and \( |a|=10 \), then \( c \) is equal to A \( \quad \pm 4 \sqrt{10} \) B \( \quad \pm 3 \sqrt{10} \) C \( \quad \pm 3 \sqrt{15} \) D \( \quad \pm 2 \sqrt{15} \) E \( \begin{array}{ll} & \pm 4 \sqrt{15}\end{array} \)
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