Pre Calculus Questions & Answers

Caladan is currently one of the world's fastest-growing countries. The exponential function \( f(x)=91(1.027)^{x} \) models the population of Caladan, \( f(x) \), in millions, \( x \) years after 1974. Using this exponential function and a calculator with a \( y^{x} \) key or a \( { }^{\wedge} \) key, answer the following questions. a. Substitute 0 for \( x \) and, without using a calculator, find Caladan's population in 1974 . 91 million Substitute 26 for \( x \) and use your calculator to find Caladan's population in the year 2000 as predicted by this function. 181.9 million (Round to the nearest tenth.) cind Caladan's population in the year 2526 as predicted by this function. million (Round to the nearest tenth.)

Caladan is currently one of the world's fastest-growing countries. The exponential function \( f(x)=91(1.021)^{x} \) modefs the population of Caladan, \( f(x) \), in millions, \( x \) years after 1974. Using this exponential function and a calculator with a \( { }^{x} \) key or a \( \wedge \) key, answer the following questions. a. Substitute 0 for \( x \) and, without using a calculator, find Caladan's population in 1974. 91 million b. Substitute 26 for \( x \) and use your calculator to find Caladan's population in the year 2000 as predicted by this function.

\( 1 \leftarrow \quad \begin{array}{l}\text { Caladan is currently one of the world's fastest-growing countries. The exponential function } f(x)=91(1.027)^{x} \text { models the } \\ \text { population of Caladan, } f(x) \text {, in millions, } x \text { years after 1974. Using this exponential function and a calculator with a } y^{x} \\ \text { key or } \mathrm{a}^{\wedge} \text { key, answer the following questions. } \\ \text { a. Substitute } 0 \text { for } x \text { and, without using a calculator, find Caladan's population in } 1974 \text {. } \\ \square \text { million }\end{array} \).

What is the range of \( f(x)=2^{-x}+2 \) ? (Type your answer in interval notation.)

What is the range of \( f(x)=4^{x}+2 \) ? (Type your answer is. interval notation.)

What is the domain of \( f(x)=4^{x}+2 ? \) \( \square \) (Type your answer in interval notation.)

17. Sebuah bola dijatuhkan dari ketinggian 8 meter. Bola memantul ke atas setelah mengenai lantai dengan ketinggian \( \frac{3}{5} \) dari ketinggian semula, begitu seterusnya. Panjang lintasan bola tersebut sampai berhenti adalah .... m . a. 18 b. 22 c. 26 d. 32 e. 36 18. Seutas tali dipotong menjadi 5 bagian sehingga panjang potongan-potongan tali tersebut membentuk barisan geometri. Jika panjang tali terpendek 6 cm dan potongan tali terpanjang 96 cm , maka panjang tali semula adalah... . a. 96 cm b. 185 cm c. 186 cm d. 191 cm e. 192 cm 19. Jika suatu deret geometri tak hingga memiliki rasio \( 2 / 3 \) dan jumlahnya adalah 18 , maka suku pertama deret tersebut adalah .... a. 4 b. 5 c. 6. d. 8 e. 12

Recall that if \( f(x)=a^{x} \), the following are true. \( \begin{array}{l}\text { - The graph of } g(x)=a^{-x}=f(-x) \text {, where } b>0 \text {, is obtained by reflecting the graph of } f \text { in the } y \text {-axis; } \\ \text { - The graph of } g(x)=-a^{x}=-f(x) \text {, where } b>0 \text {, is obtained by reflecting the graph of } f \text { in the } x \text {-axis. } \\ \text { - The graph of } g(x)=a^{x}+b=f(x)+b \text {, where } b>0 \text {, is obtained by shifting the graph of } f b \text { units upward. } \\ \text { - The graph of } g(x)=a^{x-b}=f(x-b) \text {, where } b>0 \text {, is obtained by shifting the graph of } f b \text { units to the right. } \\ \text { Determine the transformations for } g(x)=f(-x-5)=f(-(\square)) \text {. }\end{array} \) The graph of \( g \) can be obtained by reflecting the graph of \( f \) in the Select- then shifting \( f \square \)

a. Find all zeros and vertical asymptotes of the rational function \( f(x)=\frac{x+5}{(x+11)^{2}} \). If there is more than one answer, enter all such values for each in a comma separated list. If are no solutions, enter NONE. Do not leave a blank empty. (a) The function has zero(s) at \( x= \) (numbers) (b) The function has vertical asymptote(s) at \( x= \) (c) The function's long-run behavior is that \( y \rightarrow \) (d) On a piece of paper, sketch a graph of this function without using your calculator. b. How did you determine the vertical asymptote? O. By comparing the degree of the numerator and denominator. O. By dividing the polynimial and using the remainder

Describe any transformation of the graph of \( f \) that yields the graph of \( g \). \[ f(x)=13^{x}, g(x)=13^{-x-5} \] Step 1 Rewrite the function \( g \) in terms of function \( f \). \( g(x)=f(\square \)