Question

Is each of the following features of asquare root function changed by areflection across the x-axis?

Answer 1

Step-by-step 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:

`f(x)=√(x)\Rightarrow g(x)=-√(x).`

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.

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• C., The domain doesn't change, both functions are defined in the interval [x, ∞).

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• D., The range changes, f(x) has range [0,+∞) and g(x) has range [0,-∞).

Answer

A. Yes

B. No

C. No

D. Yes