Determine the domain and range for the following functions: y=x^2+5

Question

Domain and Range of y=x²+5

Answer 1

Domain means all possible x-values that you are allowed to plug into your function. The only restrictions that would affect your domain are x-values that make the denominator of a fraction equal 0, or x-values that make the value underneath a radical a negative number. Neither of these restrictions apply to this function. Therefore, the domain is all real numbers

 

Range means all possible y-values that result from the domain. The function y=x² has a range of y≥0 (If you plug in any x value within the domain into the function, you will get a y-value greater than or equal to zero). The function y=x² + 5 is the same graph as the function y=x² except raised 5 units higher. Therefore, the range is now raised five units from that of the function y=x²; so the range of y=x²+5 would be y≥5

 

Answer:

Domain: All Real Numbers

Range: y≥5