Question

given the function $n(x) = \

$$\begin{cases} x - 9 & x < -5 \\\\ 5x^2 - 2x - 2 & -5 \\leq x \\leq 1 \\\\ 4x + 5 & x > 1 \\end{cases}$$

$
calculate the following values:
$n(-1) = $
$n(7) = $
$n(-9) = $
$n(-5) = $
$n(1) = $
$n(-10) = $

Explanation:

Step1: Identify formula for $n(-1)$

$-5 \leq -1 \leq 1$, use $n(x)=5x^2-2x-2$
$n(-1)=5(-1)^2-2(-1)-2$

Step2: Compute $n(-1)$

$n(-1)=5(1)+2-2=5$

Step3: Identify formula for $n(7)$

$7>1$, use $n(x)=4x+5$
$n(7)=4(7)+5$

Step4: Compute $n(7)$

$n(7)=28+5=33$

Step5: Identify formula for $n(-9)$

$-9<-5$, use $n(x)=x-9$
$n(-9)=-9-9$

Step6: Compute $n(-9)$

$n(-9)=-18$

Step7: Identify formula for $n(-5)$

$-5 \leq -5 \leq 1$, use $n(x)=5x^2-2x-2$
$n(-5)=5(-5)^2-2(-5)-2$

Step8: Compute $n(-5)$

$n(-5)=5(25)+10-2=125+8=133$

Step9: Identify formula for $n(1)$

$-5 \leq 1 \leq 1$, use $n(x)=5x^2-2x-2$
$n(1)=5(1)^2-2(1)-2$

Step10: Compute $n(1)$

$n(1)=5-2-2=1$

Step11: Identify formula for $n(-10)$

$-10<-5$, use $n(x)=x-9$
$n(-10)=-10-9$

Step12: Compute $n(-10)$

$n(-10)=-19$

Answer:

$n(-1)=5$
$n(7)=33$
$n(-9)=-18$
$n(-5)=133$
$n(1)=1$
$n(-10)=-19$