Explanation
We must look for what features of a square-root function change when it is reflected across the x-axis. The square-root function and its reflection across the x-axis are given by:
[tex]f(x)=\sqrt{x}\Rightarrow g(x)=-\sqrt{x}.[/tex]
Plotting these functions we get the following graph:
From the graph, we see that:
• A., The end behaviour changes, f(x) tends to +∞ and g(x) tends to -∞ when x → ∞.
,
• B., The initial point location doesn't change, both functions start from the origin.
,
• C., The domain doesn't change, both functions are defined in the interval [x, ∞).
,
• D., The range changes, f(x) has range [0,+∞) and g(x) has range [0,-∞).
Answer
A. Yes
B. No
C. No
D. Yes
