Question

produce a rule for the function whose graph is shown. (hint: consider using the basic functions and the transformations of their graphs.)
$f(x) = \

$$\begin{cases} \\square & \\text{for } x < \\square \\\\ \\square & \\text{for } x \\geq \\square \\end{cases}$$

$

Explanation:

Step1: Identify split point

The function splits at $x=3$.

Step2: Find rule for $x \geq 3$

This is a horizontal line at $y=2$.
$f(x)=2$ for $x \geq 3$

Step3: Find rule for $x < 3$

This is a transformed square root: basic $\sqrt{x}$, reflected over x-axis, shifted right? No, check points: $(0,0)$, $(1,-1)$, $(4,-2)$ matches $f(x)=-\sqrt{x}$. Wait, no: $(3,-\sqrt{3}) \approx -1.73$, which aligns with the graph's left segment.
$f(x)=-\sqrt{x}$ for $x < 3$

Answer:

$$ f(x)=
LATEXBLOCK0
$$