What is the domain and range for # y = -9x + 11#?

1 Answer
Jun 21, 2018

Answer:

The domain and range are both all real numbers #RR#. See explanation.

Explanation:

The domain of a function is the largest subset of #RR#, for which the function's value can be calculated. To find the function's domain it is easier to check which points are excluded from the domain.

The possible exclusions are:

  • zeros of denominators,

  • arguments for which expressions under square root are negative,

  • arguments for which expressions under logarithm are negative,

Examples:

#f(x)=3/(x-2)#

This function has #x# in the denominator, so the value for which #x-2=0# is excluded from the domain (division by zero is impossible), so the domain is #D=RR-{2}#

#f(x)=sqrt(3x-1)#

This function has expression with #x# under square root, so the domain is the set, where

#3x-1>=0#

#3x>=1#

#x>=1/3#

The domain is #D=<1/3;+oo)#

#f(x)=-9x+11#

In this function there are no expressions mentioned in exclusions, so it can be calculated for any real argument.

To find the range of the function you can use its graph:

graph{-9x+11 [-1, 10, -5, 5]}

As you can see the function goes from #+oo# for negative numbers to #-oo# for large positive numbers, so the range is also all real numbers #RR#