Question

Which function has a domain of x>_5 and a range of y<_3?

Answer 1

c is the answer

Explanation:

Answer 2

Option C.
`y=-√(x-5)+3`

Explanation:

The complete question in the attached figure

Remember that

The domain of the function are all possible values for variable x and the range of the function are all possible values for the variable y

Case A) we have

`y=√(x-5)+3`

Remember that the discriminant must be greater than or equal to zero

For domain of this function

`(x - 5)\geq0\\x\geq5`

For range of the function

for every value of x ≥ 0

`y\geq3`

Case B) we have

`y=√(x+5)-3`

Remember that the discriminant must be greater than or equal to zero

For Domain

`(x + 5) \geq0\\x \geq(-5)`

and for every value of x ≥ (-5) range of the function will be

`y \geq (-3)`

Case C) we have

`y=-√(x-5)+3`

Remember that the discriminant must be greater than or equal to zero

For domain

`x - 5 \geq 0\\x\geq 5`

For range

`y \leq 3`

Case D) we have

`y=-√(x+5)-3`

Remember that the discriminant must be greater than or equal to zero

For domain

`(x + 5) \geq 0\\x \geq -5`

For range

`y \leq (-3)`