Question

select one: a. $f(x) = \sqrt{x - 3} - 1$ b. $f(x) = \sqrt{x - 3} + 1$ c. $f(x) = \sqrt{x + 3} - 1$ d. $f(x) = \sqrt{x + 3} + 1$

Explanation:

Step1: Identify parent function & domain

The graph is a transformed square root function. The parent function is $y=\sqrt{x}$, which has a domain $x\geq0$. The given graph starts at $x=-3$, so the domain is $x\geq-3$, meaning there is a horizontal shift left by 3 units: $\sqrt{x+3}$.

Step2: Check vertical shift & points

Test the starting point of the graph: when $x=-3$, $f(-3)=-1$. Substitute $x=-3$ into $\sqrt{x+3}+c$:
$\sqrt{-3+3}+c = 0 + c = c = -1$.
So the function is $f(x)=\sqrt{x+3}-1$. Verify another point: when $x=0$, $f(0)=\sqrt{0+3}-1=\sqrt{3}-1\approx0.73$, which matches the graph's value at $x=0$.

Answer:

C. $f(x) = \sqrt{x + 3} - 1$