Question

write an equation for the function whose graph is shown to the right. the graph above is a transformation of a common function. an equation for the function of the given graph is \boxed{\sqrt{x + 1} + 1} (type an equation using x and y as the variables. use integers or decimals for any numbers in the equation.)

Explanation:

Step1: Identify parent function

The parent function is $y=\sqrt{x}$, which has a domain $x\geq0$ and starts at $(0,0)$.

Step2: Analyze horizontal shift

The given function $\sqrt{x+1}-1$ has a horizontal shift: $x$ becomes $x+1$, which shifts the parent function left 1 unit (since $x+1=0$ gives $x=-1$, so the starting x-coordinate moves from 0 to -1).

Step3: Analyze vertical shift

The $-1$ outside the square root shifts the parent function down 1 unit, so the starting y-coordinate moves from 0 to $0-1=-1$. This means the transformed function starts at $(-1,-1)$, which matches the graph's domain and shape (a square root curve shifted left 1, down 1, consistent with the viewing window $[-2,17,1]$ by $[-2,10,1]$).

Answer:

$y=\sqrt{x+1}-1$