Question

Write a function rule for the table. X f(x) 2 3 4 -12 -16 -20 5

Answer 1

Let's assume it is a linear function of the form:

$f(x)=mx+b$

Let:

$\begin{gathered} x=2,f(x)=-8 \\ x=5,f(x)=-20 \\ ----- \\ so\colon \\ -8=2m+b_{\text{ }}(1) \\ -20=5m+b_{\text{ }}(2) \end{gathered}$

Using elimination method:

$\begin{gathered} (1)-(2) \\ -8-(-20)=2m-5m+b-b \\ 12=-3m \\ m=\frac{12}{-3} \\ m=-4 \end{gathered}$

so, replacing the value of m into (1):

$\begin{gathered} -8=2(-4)+b \\ -8=-8+b \\ b=8-8 \\ b=0 \end{gathered}$

Therefore, the function is given by:

$f(x)=-4x$