Use the image to answer the question.
Compare the given graphs of f(x) = 2 sqaure root x and g(x) = 2 3sqaure root and determine which of the following is true.
A. The graphs have different domains.
B. Both graphs go through (-1, -1), (0, 0), and (1, 1).
C. They are both decreasing on their domains.
D. When x > 1, the function g(x) = 2 3sqaure root is greater than f(x) = 2 sqaure root x
Based on the given graph, we can compare the functions f(x) = 2√x and g(x) = 2√(3x).
A. The graphs have different domains.
- The domain of f(x) is x ≥ 0, while the domain of g(x) is x ≥ 0. Both graphs have the same domain, so this statement is false.
B. Both graphs go through (-1, -1), (0, 0), and (1, 1).
- From the graph, we can see that both functions go through the points (-1, -1), (0, 0), and (1, 1). Therefore, this statement is true.
C. They are both decreasing on their domains.
- From the graph, we can see that both functions are actually increasing on their domains. Therefore, this statement is false.
D. When x > 1, the function g(x) = 2√(3x) is greater than f(x) = 2√x.
- From the graph, we can see that when x > 1, the graph of g(x) is indeed greater than the graph of f(x). Therefore, this statement is true.
Based on the analysis, the correct answer is:
D. When x > 1, the function g(x) = 2√(3x) is greater than f(x) = 2√x.