Question

Give the domain and range of the relation.
y=(x+4)^2-4

Answer 1

The domain is the interval (-∞,∞)

The range is the interval [-4,∞)

Explanation:

we have

`y=(x+4)^2-4`

This is the equation of a vertical parabola in vertex form

The vertex is the point (-4,-4)

The parabola open upward (because the leading coefficient is positive)

The vertex represent a minimum

The domain is the interval (-∞,∞)

so

The domain is all real numbers

The range is the interval [-4,∞)

`y\geq -4`

so

The range is all real numbers greater than or equal to -4