Compare the graphs of f(x)=x−−√+1 and g(x)=x−−√3+1. Which one of the following options is true? (1 point) Responses
Both functions go through the points (−1,0) and (0,1).
Both functions have the same domain, x>0.
Both functions have the same range, (−∞,∞).
Both functions are increasing on their domain.
The graph of f(x)=x−−√+1 is a square root function shifted one unit upwards. It passes through the point (-1,0) which is the vertex of the square root function. The graph decreases as x approaches negative infinity, passes through the vertex at (-1,0), and then increases as x approaches positive infinity.
The graph of g(x)=x−−√3+1 is also a square root function shifted one unit upwards. It passes through the point (-1,0) which is the vertex of the square root function. However, the coefficient of the square root function is different, so the graph of g(x) will be steeper than the graph of f(x). The graph of g(x) also decreases as x approaches negative infinity, passes through the vertex at (-1,0), and then increases as x approaches positive infinity.
Therefore, the correct option is: Both functions go through the points (-1,0) and (0,1).