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.)

Follow the seven step strategy to graph the following rational function. \( f(x)=\frac{6 x}{x-2} \) To graph the function, first determine the symmetry of the graph of f . Choose the correct answer below. y-axis symmetry origin symmetry neither \( y \)-axis symmetry nor origin symmetry What is the \( y \)-intercept? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The \( y \)-intercept is (Type an integer or a simplified fraction.)

Find the standard form of the equation of the hyperbola satisfying the given conditions. Foci at \( (0,-8) \) and \( (0,8) \); vertices at \( (0,3) \) and \( (0,-3) \)

6) O domínio da função dada por \( \mathrm{f}(\mathrm{x})= \) é a) \( \{x \in R \mid-2 \leq x \leq 3\} \). b) \( \{x \in R \mid-2 \leq x<3\} \). c) \( \{x \in R \mid 2 \leq x<3\} \). d) \( \{x \in R \mid-2 \leq x \leq 3\} \). e) \( \{x \in R \mid x \neq 3\} \).

What is the dot product of vector \( h \) with a magnitude of 5 and vector \( i \) with a magnitude of 8 if the angle between the vectors is \( \frac{\pi}{6} \) radians? (Round your answer to the nearest hundredth.)

Use transformations of the absolute value function, \( \mathrm{f}(\mathrm{x})=|\mathrm{x}| \), to graph the function \( g(x)=-|\mathrm{x}-3|-5 \). ... \( \square \) A. Horizontal shift \( \square \) B. Vertical stretch/shrink \( \square \) C. Horizontal stretch/shrink \( \square \) D. Vertical shift \( \square \) E. Reflection about the \( x \)-axis \( \square \) F. Reflection about the \( y \)-axis