Best Answer:
Just a small reminder-

Domain= All x values the function can take on. for an example, on the function 5/x, the domain is all real numbers except for zero.

Range= All y values you can get from putting in the x values in the domain. For an example, on the function x^2, you can't get negative numbers as an answer (the square root of a negative number is not a real number). In that equation, the range is x≥0.

So, in your equation- (x-1)^3+2, it's not too hard to see that you can put in ANY x value, and you'll still get a result. That's because there's no dividing by zero in here, or putting up square roots of negative numbers, or something like that.

The domain- Let's just reverse it.

y= (x-1)^3+2

y-2=(x-1)^3

(y-2)^(1/3)=x-1

(y-2)^(1/3)+1=x

So, we just reversed the equation, and the Range is simply the Domain for y.

When y is bigger or equal to 2, you just get the third root of a positive number/zero, which is easy to answer.

The third root of a negative number is also easy to answer- (-x)^(1/3) is just x^(1/3), times -1.

y can be anything in this equation.

Range- Any real number

Domain- Any real number

Hope I helped you!

Source(s):

Anonymous
· 6 years ago

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