Question

The graph of an absolute value function opens down and has a vertex of (-3,0).

The domain of the function is ?
The range of the function is ?

Answer 1

I wrote the domain and range in interval notation, not sure if that’s how you’re asked to do it. This is how I was taught to state the domain/range of a graph.

Answer 2

The domain of the function is:

All real numbers i.e. (-∞,∞)

The range of the function is:

(-∞,0]

Explanation:

It is given that:

The graph of an absolute value function opens down and has a vertex of (-3,0).

This means that the graph of the function increases continuously in the interval (-∞,-3] and takes maximum value 0 when x= -3 and then decreases continuously in the interval (-3,∞).

Domain of a function--

It is the set of all the x-values for which a function is defined i.e. it is the set of all the values of the independent variable for which the function is defined.

Range of a function--

It is the set of all the values attained by a function.

• We know that a absolute value function is defined all over the real line i.e. the domain of the function is the set of all the real values i.e. (-∞,∞).

• Also, the function takes all the value between -∞ and 0 and 0 is included.

Hence, the range of the function is: (-∞,0].