Question

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

The domain of the function is .

The range of the function is .

Answer 1

The domain of the absolute value function is all real numbers, and the range of the function is y ≥ -3.

Step-by-step explanation:

The graph of an absolute value function with a vertex at (0, -3) opens upwards. The domain of an absolute value function is always all real numbers, as it is defined for all x values. This means that the function is defined for any real number input. In this case, the domain of the given absolute value function is (-∞, ∞).

The range of an absolute value function with a vertex at (0, -3) is all y values greater than or equal to the y-coordinate of the vertex. Since the vertex has a y-coordinate of -3, the range of the function is y ≥ -3. This means that the output (or range) of the function includes all real numbers greater than or equal to -3.

In summary, the domain of the given absolute value function is all real numbers, and the range of the function is y ≥ -3.

Answer 2

The domain: all real numbers;

The range:
`y\ge -3.`

Step-by-step explanation:

The graph of the function y=|x| opens up and has a vertex at (0,0). If the graph of an absolute value function opens up and has a vertex of (0, -3), then the function has an expression

y=|x|-3 (see attached diagram).

The domain of the parent function y=|x| is the set of all real numbers, then the domain of the function y=|x|-3 is the set of all real numbers too.

The range of the parent function y=|x| is
`y\ge 0,` then the range of the function y=|x|-3 is
`y\ge -3.`