Compare the graphs of f (x) = √x +1 and g(x) = ∛x +1. Which one of the following options is true?
• Both functions go through the points (-1, 0) and (0, 1).
• Both functions are increasing on their domain.
• Both functions have the same range, (-00, co).
• Both functions have the same domain, x > 0.
The correct option is: Both functions go through the points (-1, 0) and (0, 1).
To compare the graphs of f(x) = √x + 1 and g(x) = ∛x + 1, we can analyze the behavior of these functions at certain points.
For f(x) = √x + 1:
When x = -1, the function becomes f(-1) = √(-1) + 1 = 0.
When x = 0, the function becomes f(0) = √0 + 1 = 1.
For g(x) = ∛x + 1:
When x = -1, the function becomes g(-1) = ∛(-1) + 1 = 0.
When x = 0, the function becomes g(0) = ∛0 + 1 = 1.
Both functions go through the points (-1, 0) and (0, 1), so this option is true.