Question

9 determine whether the equation represents a function.
$-(x + 2)^2 = y$
a. yes - it is a function
b. no - it is not a function

Explanation:

Step1: Recall the definition of a function

A function is a relation where each input (x - value) has exactly one output (y - value). For a given equation in terms of \(x\) and \(y\), we can use the vertical line test (or analyze the relation algebraically) to determine if it is a function. If for every \(x\) we plug into the equation, we get only one \(y\), then it is a function.

Step2: Analyze the given equation \(y=-(x + 2)^{2}\)

Let's take any real number \(x\). When we substitute a value of \(x\) into the right - hand side of the equation \(y=-(x + 2)^{2}\), we perform the operations: first, add 2 to \(x\), then square the result, and then multiply by - 1. For example, if \(x = 0\), then \(y=-(0 + 2)^{2}=-4\); if \(x=-2\), then \(y=-(-2 + 2)^{2}=0\); if \(x = 1\), then \(y=-(1 + 2)^{2}=-9\).

In general, for any real number \(x\), the expression \(-(x + 2)^{2}\) will give exactly one real number \(y\). This is because the operation of squaring a number and then multiplying by - 1 is a well - defined operation that produces a unique result for each input \(x\). So, for each input \(x\), there is exactly one output \(y\).

Answer:

A. Yes - it is a function