Finding Domain Algebraically of Square Root and Rational Function

Find the Domain of the function.

Find the Domain of the function.

Find the Domain of the function.

When considering the domain of a polynomial function, such as the one shown what restrictions must be considered?

• denominator can't be zero

• numerator can't be zero

• square root can not be negative

• no restriction for this at all

Find the domain and range of the function Graph in desmos if needed.

• Domain: (-∞, ∞)  Range: [-∞, 4]

• Domain: [1, ∞)  Range: (-∞, 4]

• Domain: [-1. ∞) Range: [4, ∞) 

• Domain: [4, ∞) Range: [-1,∞) 

Find the domain and range of the function
Hint:  Use a scratch graph to help you visualize things. 

• Domain: (-∞, ∞)  Range: [-∞, 4]

• Domain: [1, ∞)  Range: (-∞, 4]

• Domain: [-1. ∞) Range: [4, ∞) 

• Domain: [4, ∞) Range: [-1,∞) 

What is the Domain of ALL Square Root Functions?

• (−∞,∞)

• [0,∞)

• (−∞,0]

• All Square Root Functions are different.

What is the domain for: g(x) = √(x + 5) - 3

• -3 ≤ x < ∞

• − ∞ < x ≤ -3

• -5 ≤ x < ∞

• − ∞ < x ≤ -5

What is the domain for: g(x) = √(x + 5) - 3

• -3 ≤ x < ∞

• − ∞ < x ≤ -3

• -5 ≤ x < ∞

• − ∞ < x ≤ -5

What is the DOMAIN of this square root function?

• all real numbers