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Determine if the relation represents y as a function of x. If it is a function, find the domain and range.

Determine if the relation represents y as a function of x. If it is a function, find-example-1
User Ron Myschuk
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1 Answer

18 votes
18 votes

From the question we are asked to determine if the relation represents y as a function of x. If it is a function, find the domain and range.

y = √-x - 4

To determine if its a function, it has passed the vertical line test, so yes its a function.

if a vertical line touches the graph at more than one point then it's a function.

Domain of √-x - 4:

√f(x) ----> f(x) ≥ 0

solve for -x ≥ 0: x ≤ 0

Domain: x ≤ 0

For the range of √-x - 4

recall the range of a radical function of the form:

c√(ax + b) + k is f(x) ≥ k

k = -4

f(x) ≥ -4

So, Domain {x ≤ 0}: Range: {y ≥ -4}

So, the correct option is the third option which is {x ≤ 0}: Range: {y ≥ -4}

Grpah:

Determine if the relation represents y as a function of x. If it is a function, find-example-1
User McKinley
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