Question

Radicals and Exponents Which if the following functions might have a graph like the following

Answer 1

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.

`\begin{gathered} f(x)=\sqrt[]{x-1}-2 \\ f(0)=\sqrt[]{0-1}-2 \\ f(0)=\sqrt[]{-1}-2 \\ f(0)=-2i \end{gathered}`

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.

`\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}`

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.