Sketch the graph of the exponential function \( g(x) = 3^{x-1} + 2 \), indicating its asymptote.

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. \%

Which transformations must be applied to obtain the graph of \( f(x)=5^{x+4} \) ? Select all that apply. \( \square \) A. Horizontal compression or stretch \( \square \) B. Reflection about the \( y \)-axis \( \square \) C. Reflection about the \( x \)-axis \( \square \) D. Vertictal shift \( \square \) E. Vertical compression or stretch \( \square \) F. Horizontal shift

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

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. \( f(x)=\frac{x-7}{2}, g(x)=|-x| \)