Question

evaluate the function for the indicated values
$f(x)= \

$$\begin{cases} 2x + 1, & x \\leq -5 \\\\ x^2, & -5 < x < 5 \\\\ 3 - x, & x \\geq 5 \\end{cases}$$

$
$f(-10)= \square$
$f(2)= \square$
$f(-5)= \square$
$f(-1)= \square$
$f(8)= \square$

Explanation:

Step1: Evaluate $f(-10)$ (use $2x+1$)

Since $-10 \leq -5$, substitute $x=-10$ into $2x+1$:
$2(-10)+1 = -20+1 = -19$

Step2: Evaluate $f(2)$ (use $x^2$)

Since $-5 < 2 < 5$, substitute $x=2$ into $x^2$:
$2^2 = 4$

Step3: Evaluate $f(-5)$ (use $2x+1$)

Since $-5 \leq -5$, substitute $x=-5$ into $2x+1$:
$2(-5)+1 = -10+1 = -9$

Step4: Evaluate $f(-1)$ (use $x^2$)

Since $-5 < -1 < 5$, substitute $x=-1$ into $x^2$:
$(-1)^2 = 1$

Step5: Evaluate $f(8)$ (use $3-x$)

Since $8 \geq 5$, substitute $x=8$ into $3-x$:
$3-8 = -5$

Answer:

$f(-10) = -19$
$f(2) = 4$
$f(-5) = -9$
$f(-1) = 1$
$f(8) = -5$