How do you find the domain and range of #g(t) = 5t#?

1 Answer
Mar 24, 2017

Answer:

See explanation.

Explanation:

Domain

The domain is the largest subset of real numbers #RR# for which the function is defined. To find it we have to look for any possible values of #x# for which the function is undefined.

The possible exclusions are:

  • zeroes of denominators,

  • values for which expressions under square root sign (or other roots with an even degree) are negative

  • values for which expressions under logarythm signs are negative or zero

The given function does not contain any of the limitations mentioned above, therfore its domain is #RR#

Range

To find the range we have to look for possible values of the function. From the formula we see that the values can be all numbers in #RR#. As the arguments go to minus infinity, the values also go to minus infinity. The situation is simmilar when #x# goes to plus infinity. The values also grow up to plus infinity.
So the range is also #RR#