Use transformations to graph the function \( f(x)=4^{x+4} \). Determine its domain, range, and horizontal asymptote. Which transformations must be applied to obtain the graph of \( f(x)=4^{x+4} \) ? Selec all that apply. \( \square \) A. Horizontal compression or stretch \( \square \) B. Reflection about the \( x \)-axis \( \square \) C. Vertical shift \( \square \) D. Vertical compression or stretch \( \square \) E. Horizontal shift \( \square \) F. Reflection about the \( y \)-axis

To graph the function \( f(x) = 4^{x+4} \), we first note that this is an exponential function which inherently has a domain of all real numbers, \( (-\infty, \infty) \). The range is \( (0, \infty) \) as exponential functions never touch or cross the x-axis. The horizontal asymptote is at \( y = 0 \). To obtain the graph of \( f(x) = 4^{x+4} \), you would apply a horizontal shift to the left by 4 units. Thus, the relevant transformations are: - E. Horizontal shift Additionally, the function shows vertical stretch since the base (4) is greater than 1, which implies that the correct answers are D. Vertical compression or stretch (specifically a vertical stretch in this case). So, you can check E and D; the changes represent shifting and stretching the base function \( 4^x \).