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

Jun 21, 2018

The domain and range are both all real numbers $\mathbb{R}$. See explanation.

#### Explanation:

The domain of a function is the largest subset of $\mathbb{R}$, 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:

## $f \left(x\right) = \frac{3}{x - 2}$

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 $D = \mathbb{R} - \left\{2\right\}$

## $f \left(x\right) = \sqrt{3 x - 1}$

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

$3 x - 1 \ge 0$

$3 x \ge 1$

$x \ge \frac{1}{3}$

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

## $f \left(x\right) = - 9 x + 11$

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 $+ \infty$ for negative numbers to $- \infty$ for large positive numbers, so the range is also all real numbers $\mathbb{R}$