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Home Question Bank Math Pre Calculus Archive 2024 December 20

Pre-calculus Questions from Dec 20,2024

Browse the Pre-calculus Q&A Archive for Dec 20,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Simplify \( \frac{\left(1-\frac{1}{2^{2}}\right)\left(1-\frac{1}{3^{2}}\right)\left(1-\frac{1}{4^{2}}\right) \ldots\left(1-\frac{1}{2005^{2}}\right)}{\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right) \ldots\left(1-\frac{1}{2005}\right)} \) Consider the function \( y=\sqrt{4-x} \). What are the domain and range of this function? domain: \( x \leq 4 \), range: \( y \geq 0 \) domain: \( x \geq 2 \), range: \( y \geq 2 \) domain: \( x \leq 2 \), range: \( y \geq 2 \) With exponential functions of the form \( y=a \cdot b^{-x} \), as \( x \) goes to positive infinity, the \( y \)-values tend towards a.) positive infinity b.) one c.) zero d.) negative infinity Convert to radian measure. Leave the answer in terms of \( \pi \). \( 280^{\circ} \) \( 280^{\circ}=\square \) radians (Simplify your answer. Use integers or fractions for any numbers in the expression.) Evaluate or simplify the expression without using a calculator. \( e^{\ln 134} \) \( e^{\ln 134}=\square \) 14. Convert \( 171^{\circ} \) to radians. If \( f(x)=\frac{\sqrt{x+2}}{3-3 x^{2}} \), for which values of \( x \) is \( \begin{array}{ll}1.2 .2 & f(x) \text { non real. } \\ 1.2 .3 & f(x) \text { undefined } \\ 1.2 .4 & f(x)>0\end{array} \) 9. Graph \( f(x)=\left\{\begin{array}{cc}x^{2}, & x \leq 2 \\ 4, & x=2 \\ 10-x, & x>2\end{array}\right. \) 7. Graph \( f(x)=-\frac{1}{2}(x-1)^{2} \) Question/ Which of the following functions has removable discontinuity at \( x=2 \) ? \( \begin{array}{llll}\text { (A) } f(x)=\frac{x^{2}+4}{x-2} & (B) f(x)=\frac{|x+2|}{x+2} & \text { (C) } f(x)=\frac{3 x^{2}-12}{2 x-4} & \text { (D) } f(x)=\frac{x+2}{x^{2}-4}\end{array} \)
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