Draw the graph of the function and state the domain and range. \( f(x)=5^{x}+3 \)

To draw the graph of the function \( f(x) = 5^x + 3 \), start by plotting key points. At \( x = 0 \), \( f(0) = 5^0 + 3 = 4 \); at \( x = 1 \), \( f(1) = 5^1 + 3 = 8 \); and at \( x = -1 \), \( f(-1) = 5^{-1} + 3 = 3.2 \). As \( x \) approaches negative infinity, \( f(x) \) approaches 3, which gives the horizontal asymptote. The graph will rise steeply as \( x \) increases, demonstrating its exponential nature. The domain of \( f(x) \) is all real numbers, \( (-\infty, \infty) \), since you can input any real number for \( x \). The range is \( (3, \infty) \), as the function approaches but never reaches the value of 3 and continues to increase without bound.