Question

I can give the options, I just need the correct answer explained please...

Answer 1

Given the function;

`\begin{gathered} f(x)=-3\sqrt[]{x+1} \\ x=\mleft\lbrace-1,0,3,8,15\mright\rbrace \end{gathered}`

To complete a table that could be used to graph the function, we substitute each value of x in the function to get its corresponding y value. We have;

`\begin{gathered} \text{When x=-1;} \\ f(-1)=-3\sqrt[]{-1+1} \\ f(-1)=-3\sqrt[]{0} \\ f(-1)=0 \\ \text{When x=0;} \\ f(0)=-3\sqrt[]{0+1} \\ f(0)=-3\sqrt[]{1} \\ f(0)=-3 \end{gathered}`

Also,

`\begin{gathered} \text{When x=3;} \\ f(3)=-3\sqrt[]{3+1} \\ f(3)=-3\sqrt[]{4} \\ f(-3)=-6 \\ \text{When x=8;} \\ f(8)=-3\sqrt[]{8+1} \\ f(8)=-3\sqrt[]{9} \\ f(8)=-9 \\ \text{When x=15;} \\ f(15)=-3\sqrt[]{15+1} \\ f(15)=-3\sqrt[]{16} \\ f(15)=-12 \end{gathered}`

Thus, the table is given as;