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How do you find the range of the given function with domain D where #g: x → 1 - x^2#, D = {-1 , 0, 1}?

Answer 1

To find the elements in the Range,R when D (the domain) is a collection of discrete values, as it is in this example, just evaluate the function for each of those values (duplicate values may occur but they can be ignored)

#g:-1 rarr 0# #g:0 rarr 1# #g:1 rarr 0#

R #= {0,1}#

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Answer 2

Ethan Adkins

To find the range of the function g(x) = 1 - x^2 with the domain D = {-1, 0, 1}, we substitute each value in the domain into the function and determine the corresponding output values. Then, we identify the minimum and maximum values among these outputs, which constitute the range.

Substituting -1, 0, and 1 into the function yields: g(-1) = 1 - (-1)^2 = 1 - 1 = 0 g(0) = 1 - (0)^2 = 1 - 0 = 1 g(1) = 1 - (1)^2 = 1 - 1 = 0

The range of the function g(x) with the given domain D is {0, 1}.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.