Question

Find the range of the function. f(x) = (x - 2)^2 + 2

Answer 1

ok

Answer 2

function is a rule that associates an element from one set to another, most often both sets are real numbers, such that for every element in the domain set there is a unique element in the target set. You have been given a function from the set of real numbers to the set of real numbers and they have defined the domain.

Function: f(x) = x^2 + 3. ('^' denotes that the number following is an exponent)

Domain: {x | x>=2}

The domain notation is just a fancy way of writing that any real number greater than or equal to 2 is a valid input for your function. They want the range of the function. The range is an interval which, no matter what value of the domain you choose as an input, the function's output will fall between. It is easy to see that the function is strictly increasing, so the lower bound is the value of f(x) when x is 2.

f(2) = 2^2 + 3 = 7

Because f is increasing, and the domain has no upper bound, then the range has no upper bound. So on the domain [2,infinity), the range is [7,infinity). Written in set notation:

Range = {y | y>=7}

Answer 3

got it

Answer 4

thank you so much!!!

Answer 5

your welcome