When there are no restrictions the domain of a function

Last updated: 5/25/2023

When there are no restrictions the domain of a function consists of all real numbers because there are no exclusions The inputs come from all values on the real number line which span from negative infinity to positive infinity Enter the domain of the function y x2 8 using interval notation 0 00 0 Nice work Step 3 The range of a function consists of all real number outputs that result from inputting the values in the domain of the function which is Because the square of a real number is nonnegative x must be nonnegative In other words x Thus x has a least value but there is no greatest value because the range increases toward infinity If our function were only y x then zero would be the least value in the range of y However the function is y x 8 which increases x by 8 This will also increase the lower limit in the range by 8 as follows x 8 0 The upper limit of the range has not changed as y increases toward infinity Enter the range for the function y x 8 using interval notation