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Evaluate pleaseeee thank you!

Evaluate pleaseeee thank you!-example-1

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Answer:

f(-4) = -2

f(-5) = 1

Explanation:

Given piecewise function:


f(x)=\begin{cases} (x+3)^2-3&amp;\;\;\text{for}\;\;x < -3\\-1&amp;\;\;\text{for}\;\;x=-3\\-x-7&amp;\;\;\text{for}\;\;x > -3\end{array}

A piecewise function is a function that uses different equations for different parts of its domain.

To find f(-4), we need to use the equation where the domain includes x = -4. Since x = -4 is in the interval x < -3, we can use the equation f(x) = (x + 3)² - 3 to find f(-4).

Therefore, to calculate f(-4), substitute x = -4 into this equation:


\begin{aligned}f(-4)&amp;=((-4)+3)^2-3\\&amp;=(-4+3)^2-3\\&amp;=(-1)^2-3\\&amp;=1-3\\&amp;=-2\end{aligned}

Similarly, x = -5 is also in the interval x < -3, so we use the same equation to find f(-5), this time substituting x = -5:


\begin{aligned}f(-5)&amp;=((-5)+3)^2-3\\&amp;=(-5+3)^2-3\\&amp;=(-2)^2-3\\&amp;=4-3\\&amp;=1\end{aligned}

Evaluate pleaseeee thank you!-example-1
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