Give domain and range of the graph of

Question

f(x)= 5/(x+2)² + 3

Answer 1

f(x)= 5/(x+2)² + 3

Domain is the set of allowable values for the independent variable ( x in this equation). Looking at the function, there is a solution everywhere except x = -2, where f(x) is not defined. So the domain is simply x ≠ -2.

The range is the possible values for f(x). Try some values for x:

If x is large, the first term tends to 0, and f(x) is asymptotic to 3 (from the high side). The same thing happens if x is a large negative number.

The range of g(x) appears to be g(x) > 3

CHECK this by graphing the function

Answer 2

f(x) = 5/(x+2)² + 3

Since we can't divide by zero, the domain is the set of all real numbers not equal to -2.

5/(x+2)² is always positive. So, 5/(x+2)² + 3 is always greater than 3. Therefore, the range is the set of all real numbers greater than 3.