Graph the function \( f(x)=6^{x}-3 \). Give the domain and range. Which transformation is needed to graph the function \( f(x)=6^{x}-3 \) ? Choc A. The graph of \( f(x)=6^{x} \) should be shifted up 3 units. B. The graph of \( f(x)=6^{x} \) should be shifted to the left 3 units. D. The graph of of \( f(x)=6^{x} \) should be shifted down 3 units. Use the graphing tool to graph the function. The domain of the function \( f(x)=6^{x}-3 \) is (Type your answer in interval notation.)

To graph the function \( f(x) = 6^x - 3 \), you start with the basic exponential function \( f(x) = 6^x \). The transformation needed is to shift the graph **down 3 units** since you’re subtracting 3 from \( 6^x \). So, the correct answer is D! The domain of the function \( f(x) = 6^x - 3 \) is all real numbers, which can be expressed in interval notation as \( (-\infty, \infty) \). This means there are no restrictions on the value of \( x \) that can be plugged into the function. Now, let's move on to some fun facts! Did you know that exponential functions like \( 6^x \) can model real-world phenomena such as population growth or radioactive decay? In these cases, the base often represents the growth rate, and the exponent illustrates time passed, making these functions incredibly useful for modeling dynamic systems in nature! Another great way to ensure you're not making mistakes while graphing exponential functions is to identify key points. Starting with \( x = 0 \) can be a game changer — it gives you \( f(0) = 6^0 - 3 = -2 \). Plotting these key points helps form a clear picture of the graph before shifting it down! Always double-check against your key points!