Question

Evaluate pleaseeee thank you!

Answer 1

f(-4) = -2

f(-5) = 1

Explanation:

Given piecewise function:

`f(x)=\begin{cases} (x+3)^2-3&\;\;\text{for}\;\;x < -3\\-1&\;\;\text{for}\;\;x=-3\\-x-7&\;\;\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)&=((-4)+3)^2-3\\&=(-4+3)^2-3\\&=(-1)^2-3\\&=1-3\\&=-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)&=((-5)+3)^2-3\\&=(-5+3)^2-3\\&=(-2)^2-3\\&=4-3\\&=1\end{aligned}`