1 Graphen Zeichne die Graphen folgender Exponentialfunktionen: \( \begin{array}{ll}\text { a) } f(x)=2^{x} & \text { e) } f(x)=2^{x}+1 \\ \text { b) } f(x)=3 \cdot 2^{x} & \text { f) } f(x)=2^{x}-1 \\ \text { c) } f(x)=\left(\frac{1}{2}\right)^{x} & \text { g) } f(x)=\left(\frac{1}{2}\right)^{x}+3 \\ \text { d) } f(x)=3 \cdot\left(\frac{1}{2}\right)^{x} & \text { h) } f(x)=3 \cdot\left(\frac{1}{2}\right)^{x}-2\end{array} \)

Find functions \( f \) and \( g \) so that \( f \circ g=H \). \( H(x)=|2 x+7| \) Choose the correct pair of functions. A. \( f(x)=|x|, g(x)=2 x+7 \) B. \( f(x)=|-x|, g(x)=\frac{x-7}{2} \) C. \( f(x)=2 x+7, g(x)=|x| \) D. \( f(x)=\frac{x-7}{2}, g(x)=|-x| \)

Find the vertical, horizontal, and oblique asymptotes, if any, for the following rational function. \( R(x)=\frac{9 x}{x+8} \)

Find the domain of the function. \[ g(x)=\ln (x-7) \] The domain of \( g \) is (Type your answer in interval notation.)

Which of the following exponential functions is an increasing function? Choose the correct answer below. \( f(x)=\left(\frac{5}{2}\right)^{x} \) \( f(x)=0.3^{x} \) \( f(x)=\left(\frac{2}{7}\right)^{x} \) \( f(x)=0.8^{x} \)

The function modeling this situation is \( y=100 \cdot \mathbf{0 . 1 3 5}{ }^{2} \). Calculate the percent of light available at a depth of 29 inches. \%