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 \( f \square \)

What is the direction of a vector with a horizontal component of 2 and a vertical component of -4 ?

Where is there a discontinuity / are there discontinuities (holes or asymptotes) in the rational function \( f(x)=\frac{x^{2}+3 x+2}{x^{2}-4} ? \) \( x= \) 0 \( x= \) 2 \( x= \) -2 \( x=2 \) -2 \( x=0 \) \( 2,-2 \) \( x \)

The number of U.S. travelers to other countries during the period from 1990 through 2009 can be modeled by the polynomial function \( P(x)=-0.00530 x^{3}+0.1366 x^{2}+1.250 x+46.49 \) where \( x=0 \) represents \( 1990, x=1 \) represents 1991 , and so on and \( P(x) \) is in millions. Use this function to approximate the number of \( U \).S. travelers to other countries in each given year. (a) 1990 (b) 2000 (c) 2009 (a) In 1990 , the number of U.S. travelers to other countries was approximately \( \square \) million. (Simplify your answer. Type an integer or decimal rounded to the nearest tenth as needed.) (b) In 2000, the number of U.S. travelers to other countries was approximately \( \square \) million. (Simplify your answer. Type an integer or decimal rounded to the nearest tenth as needed.) (c) In 2009, the number of U.S. travelers to other countries was approximately \( \square \) million. (Simplify your answer. Type an integer or decimal rounded to the nearest tenth as needed.)

Select your answer What is the direction of a vector with a horizontal component of -2 and a vertical component of -4 ? \( -63^{\circ} \) \( -117^{\circ} \) 0.

What is the magnitude of a vector with a horizontal component of 5 and a vertical component of \( 12 ? \)