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Determine whether the equation defines y as a function of x x+9=y^2 Does the equation define yas a function of x? Yes No

Pergunta

Determine whether the equation defines y as a function of x
x+9=y^2
Does the equation define yas a function of x?
Yes
No

Determine whether the equation defines y as a function of x x+9=y^2 Does the equation define yas a function of x? Yes No

Solução

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LeandroElite · Tutor por 8 anos

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Explicação

## Step 1<br />The problem asks us to determine whether the equation \(x+9=y^{2}\) defines \(y\) as a function of \(x\). In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.<br /><br />## Step 2<br />To determine if \(y\) is a function of \(x\), we need to check if for every \(x\) there is exactly one \(y\). <br /><br />## Step 3<br />In the given equation, \(x+9=y^{2}\), for a given \(x\), there can be two possible values of \(y\), one positive and one negative. This is because the square root of a number can be both positive and negative.<br /><br />## Step 4<br />Therefore, the equation does not define \(y\) as a function of \(x\).
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