Use transformations to graph the function. Determine the domain, range, horizontal asymptote, and \( y \)-intercept of the function. \( f(x)=4^{x}+3 \) Use the graphing tool to graph the function. What is the domain of \( f(x)=4^{x}+3 \) ? (For any answer boxes shown with the grapher, type an exact answer.) (Type your answer in interval notation.)

What is the range of \( y=-5 \sin (x) \) ? all real numbers \( -5 \leq y \leq 5 \) all real numbers \( -\frac{5}{2} \leq y \leq \frac{5}{2} \) all real numbers \( -1 \leq y \leq 1 \) all real numbers \( -\frac{1}{5} \leq y \leq \frac{1}{5} \)

A weight attached to a spring is at its lowest point, 9 inches below equilibrium, at time \( t=0 \) seconds. When the weight it released, it oscillates and returns to its original position at \( t=3 \) seconds. Which of the following equations models the distance, \( d \), of the weight from its equilibrium after \( t \) seconds? \( d=-9 \cos \left(\frac{\pi}{3} t\right) \) \( d=-9 \cos \left(\frac{2 \pi}{3} t\right) \) \( d=-3 \cos \left(\frac{\pi}{9} t\right) \) \( d=-3 \cos \left(\frac{2 \pi}{9} t\right) \)

State the equation of \( f(x) \) if its domain is \( \{x \in R \mid x \neq 0\} \), the \( y \)-intercept does not exist, and the equation of the horizontal asymptote is \( y=1 \).

State the equation of \( f(x) \) if its domain is \( \{x \in R \mid x \neq 0\} \), the \( y \)-intercept does not exist, and the equation of the horizontal asymptote is \( y=1 \).

\begin{tabular}{|l|}\hline 3. Find the standard equation for the hyperbola \\ that has foci \( (0, \pm 5) \) and vertices \( (0, \pm 3) \). \end{tabular}