Answer:
Step-by-step explanation:
rI'm sorry, but the question you provided seems to be incomplete and contains some formatting errors. However, I can help you understand the given function and its transformations. The given function is g(x) = √(x-2) - 5. To describe its transformations, we need to compare it to the parent function f(x) = x. First, let's start with the parent function f(x) = x. This is a basic linear function that has a slope of 1 and passes through the origin (0, 0). Now, let's look at the given function g(x) = √(x-2) - 5. The transformation of g(x) compared to f(x) involves three steps: 1. Horizontal translation: The function g(x) has a horizontal translation of 2 units to the right compared to the parent function f(x). This means that the graph of g(x) is shifted 2 units to the right. 2. Vertical translation: The function g(x) has a vertical translation of 5 units downward compared to the parent function f(x). This means that the graph of g(x) is shifted 5 units downward. 3. Square root function: The function g(x) includes a square root function, which affects the shape of the graph. The square root function causes the graph to be "curved" instead of a straight line. To graph g(x) along with the parent function f(x), you would first plot the points for the parent function f(x) = x: (N, N), (2, 0), (0, 0), (-2, 0), and (-N, -N). Next, you would apply the transformations to each point. For the horizontal translation, add 2 units to the x-coordinate of each point. For the vertical translation, subtract 5 units from the y-coordinate of each point. Finally, plot the transformed points to graph g(x). To find the domain of g(x), we need to consider the restrictions of the square root function. Since we cannot take the square root of a negative number, the expression inside the square root, (x-2), must be greater than or equal to 0. Solving this inequality, we find that x must be greater than or equal to 2. Therefore, the domain of g(x) is all real numbers greater than or equal to 2. I hope this explanation helps you understand the given function and its transformations. If you have any further questions, please feel free to ask!
