Question

Find the value of k in the data set so that it becomes a linear function.

Answer 1

Notice that for each increase in 4 units of the variable x, the function f(x) increases by 5 units.

Then:

`\begin{gathered} f(-2)+5=f(-2+4) \\ \\ \Rightarrow f(-2)+5=f(2) \\ \\ \Rightarrow f(-2)=f(2)-5 \\ \\ \Rightarrow f(-2)=2-5 \\ \\ \therefore\quad f(-2)=-3 \end{gathered}`

Therefore, k=-3.