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

Find the domain of the function. \[ f(x)=\ln \left(x^{2}-121\right) \] Write the domain in interval notation. The domain is \( \square \).

El conjunto de positividad de \( f(x)=\ln \left(x^{2}-15\right) \)

3) \( f(x)=\left\{\begin{array}{ll}-2^{x}, & x<-4 \\ -|x|, & -4 \leq x \leq 0 \\ 4-x^{2}, & x>0\end{array}\right. \)

Let \( f(x)=7\left(\frac{1}{2}\right)^{x} \). Complete parts (a) through (e) below. (e) Is f a one-to-one function? Does fhave an inverse?

Let \( f(x)=7\left(\frac{1}{2}\right)^{x} \). Complete parts (a) through (e) below. (a) What are the domain and range of \( f \) ? The domain of \( f \) is \( \square \) and the range of \( f \) is (Type your answers in interval notation.) (b) Is f either increasing or decreasing on its domain?