Question

-Where does the graph of f(x) = -3√-2x - 3 start?OA. (-2,3)OB. (-3)OC. (-1,0)OD. (1,3)Reset Selection

Answer 1

In general, the domain of the square root function is

`domain(√(y))=\lbrack0,\infty)`

Therefore, for f(x) to be well defined, we need the radicand to be more or equal to 0; this is

`\begin{gathered} -2x-3\ge0 \\ \Rightarrow-2x\ge3 \\ \Rightarrow x\leq(3)/(-2) \end{gathered}`

Thus, finding the corresponding value of f(x) for x=-3/2

`\begin{gathered} \\ \Rightarrow f(-(3)/(2))=-3\sqrt{-2(-(3)/(2))-3}=-3√(3-3)=0 \\ \Rightarrow(-(3)/(2),0) \end{gathered}`

Hence, the answer is option C. (-3/2,0)