Question

answer attempt 1 out of 2
$f(x)=\

$$\begin{cases} \\boxed{\\phantom{0000}} \\text{for} \\boxed{\\phantom{000}} \\end{cases}$$

$

Explanation:

Step1: Identify first piece of function

The left horizontal segment has a constant value of 4, and it extends to all $x$ values less than 1 (open circle at $x=1$, $y=4$).
<Expression>$f(x)=4$ for $x<1$</Expression>

Step2: Identify second piece of function

The right segment is a line starting at an open circle at $x=1$, $y=6$, with a slope of 1. Using point-slope form $y-y_1=m(x-x_1)$:
<Expression>$f(x)-6=1(x-1) \implies f(x)=x+5$ for $x>1$</Expression>

Answer:

$$f(x) =
LATEXBLOCK0
$$