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

Aug 30, 2017

domain: all real numbers.
range: all real numbers y such that $0 \le y$

#### Explanation:

The domain of the function is the set of all values x for which the function is defined. Generally, any value of x which would cause a divide by zero is excluded.

Function $g \left(x\right)$ does not involve a divide operation, so therefore there are no values of x that would be excluded. The domain of $g \left(x\right)$ is therefore all real numbers.

The range of the function is the set of all output values that could be produced by the function.

Function g(x) is an absolute value, so therefore no negative values will ever be produced by the function.

At $x = - 5$, the value of $g \left(x\right) = 0$, which is the minimum value.
the range of the function g(x) is therefore the set of all numbers y such that $0 \le y$.

...always good to have a graph of the function as a "sanity check".

graph{|x+5| [-10, 10, -5, 5]}

GOOD LUCK!