State the domain and range of the function. (Enter your answers using interval notation.) y = √x + 9

Solution:

For an ordered pair (x, y) that a set contain:

x = domain 

y = range

In a relation x can have 2 or more than 2 ranges.

So, domain = first element of ordered pair

When, we find the domain of a root, we first have to set it to ≥ 0, as a root of something can’t be a negative number.

So, √x + 9 ≥ 0 

On simplification,

x + 9 ≥ 0 

x ≥ -9

Domain of the function is [-9, ∞] 

We know that f(-9) = 0 

The value of the function increases as x increases without any upper limit.

Range = [0, ∞]

Therefore, the domain and range of the function is [-9, ∞] and [0, ∞] respectively.

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State the domain and range of the function. (Enter your answers using interval notation.) y = √x + 9

Summary:

The domain and range of the function y = √x + 9 using interval notation is [-9, ∞] and [0, ∞] respectively.