Based on the graph, the y-intercept is a negative number. Hence, the function should either be A or B.
Let's check which of the two gives us the given graph. Let's assume x = 0.
Let's start with A.
[tex]\begin{gathered} f(x)=\sqrt[]{x-1}-2 \\ f(0)=\sqrt[]{0-1}-2 \\ f(0)=\sqrt[]{-1}-2 \\ f(0)=-2i \end{gathered}[/tex]
As we can see in Option A, if we plug in x = 0, the value of f(x) is an imaginary number hence, for this equation A, there's no y-intercept.
Because Function A doesn't have a y-intercept, then, the function that might have graph like in the image is Function B.
To be sure, let's check and plug in x = 0 in Function B.
[tex]\begin{gathered} f(x)=\sqrt[]{x+1}-2 \\ f(0)=\sqrt[]{0+1}-2 \\ f(0)=\sqrt[]{1}-2_{} \\ f(0)=1-2 \\ f(0)=-1 \end{gathered}[/tex]
As we can see above, at x = 0, f(x) = -1. The y-intercept is a negative number which is similar to the graph shown.
Hence, the answer is Function B.
