Question

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

Answer 1

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`