Question

The table represents the function f(x) .

Answer 1

Answer:

The answer you are looking for is A: f(x)=2/3t+4

Step-by-step explanation:

Answer 2

Answer:

The function f(t) is given by:

                      $f(t)=\dfrac{2}{3}t+4$

Step-by-step explanation:

We are given a table of values as:

           x     f(x)

          -6      0

          -3      2

           0       4

           3       6

           6       8        

As we could see that in each of the options the function is linear.

Hence, we will find the equation of the function f(t) by choosing two points.

We know that the equation of a line passing through two points (a,b) and (c,d) is calculated by:

$y-b=\dfrac{d-b}{c-a}\times (x-a)$

Here let (a,b)=(-6,0) and (c,d)=(0,4)

Hence, the equation of line is:

$y-0=\dfrac{4-0}{0-(-6)}(x-(-6))\\\\\\y=\dfrac{4}{6}\times (x+6)\\\\\\y=\dfrac{4}{6}x+\dfrac{4}{6}\times 6\\\\\\y=\dfrac{2}{3}x+4$

         Hence, the function f(t) is given by:

                     $f(t)=\dfrac{2}{3}t+4$