Question

Write a function for the data given in the table

Answer 1

The function of the data is $f(x)=-\frac{3}{2} x+\frac{3}{2}$.

Solution:

Let y = f(x)

Take any two points on the table.

(-3, 6) and (3, -3)

So $x_1=-3, y_1=6, x_2=3, y_2=-3$

Slope of the line:

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{-3-6}{3-(-3)}$

$m=\frac{-9}{6}$

$m=-\frac{3}{2}$

Using point-slope formula:

$y-y_1=m(x-x_1)$

$y-6=-\frac{3}{2} (x-(-3))$

$y-6=-\frac{3}{2} (x+3)$

$y-6=-\frac{3}{2} x-\frac{9}{2}$

Add 6 from both sides, we get

$y=-\frac{3}{2} x+\frac{3}{2}$

$f(x)=-\frac{3}{2} x+\frac{3}{2}$

The function of the data is $f(x)=-\frac{3}{2} x+\frac{3}{2}$.