How do you find the range of each function given the domain: #f(x)=-x/3+1;{-3,0,6}#?

Answer 1

Range; #color(green)({2,1,-1})#

Given a domain composed of a set of discrete values the range is the set of values generated by evaluation of the function for the set of domain values.

#f(x)=-x/3+1# Domain: #x in {-3,0,6}#

Range: #{f(-3), f(0), f(6)} = {2, 1,-1}#

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Answer 2

Isaiah Anthony

To find the range of the function ( f(x) = -\frac{x}{3} + 1 ) given the domain {-3, 0, 6}, you evaluate the function at each value in the domain and determine the corresponding output values. Then, you identify the minimum and maximum values of the outputs to determine the range. So, by substituting each value in the domain into the function, you get:

( f(-3) = -\frac{-3}{3} + 1 = 2 )
( f(0) = -\frac{0}{3} + 1 = 1 )
( f(6) = -\frac{6}{3} + 1 = -1 )

Thus, the range of the function for the given domain is {2, 1, -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.