Sketch the graph y=xradical4-x^2 Not allowed to use graphing calculator

Question

y=xradical4-x^2     Notes: 4-x^2 is all under radical

 

 

Not allowed to use graphing calculator. I am supposed to figure out how the graph is going to be by the "domain, intercepts, asymptotes, intervals of Increase/decrease, Local extrema and concavity and inflection points."

 

 

Answer 1

If 4 - x² is under the square root symbol, it cannot be allowed to go negative.

So the domain must be |x|≤ 2.  Interval notation: [-2,2]

The graph will be the upper half of a circle of radius 2, centered at the origin.

By simple observation of the graph, you can determine most of the requested answers.

No inflection point since concavity never changes.

 

This may also be done using things you learn in Calculus. However, my remarks are confined to skills learned in Algebra II or College Algebra.