What is domain and range of #y=-sqrt(4-x^2)# ?

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#y=-sqrt(4-x^2)#

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Answer 1 · 2018-05-06T13:20:34

#color(green)("The range of " -sqrt(4 - x^2) " at the domain interval " -2 <= x <= 2 " is " -2 <= f(x) <= 0#

#color(crimson)("The Domain of a function is the set of input or argument values for the function to be real and defined."#

#y = -(4 - x^2)#

#4 - x^2 >= 0" : " -2 <= x <= +2#

#"Interval Notation : ' [-2, 2]#

#color(purple)("Function Range Definition : The set of values of the dependent variable for which a function is defined."#

#"Compute the values of the function at the edges of the interval"#

#"The interval has a maximum point with value f(-2) = 0 "#

#"The interval has a minimum point with value f(0) = -2 "#

#"The interval has a maximum point with value f(2) = 0 "#

#"Combine the function vale at the edge with the extreme points of the function in the interval."#

#"Minimum function value at the domain interval " -2 <= x <= 2 " is " -2#

#"Maximum function value at the domain interval " -2 <= x <= 2 " is " 0#

#:. color(green)("the range of " -sqrt(4 - x^2) " at the domain interval " -2 <= x <= 2 " is " -2 <= f(x) <= 0#

graph{- sqrt(4 - x^2) [-9.29, 10.71, -5.56, 4.44]}