the function represented in the table below follows a linear pattern.\n| x | f(x) |\n| 3 | -4 |\n| 5 | -6…

the function represented in the table below follows a linear pattern.\n| x | f(x) |\n| 3 | -4 |\n| 5 | -6 |\n| 7 | -8 |\nwhat is the rate of change?\nwhat is f(7)?

the function represented in the table below follows a linear pattern.\n| x | f(x) |\n| 3 | -4 |\n| 5 | -6 |\n| 7 | -8 |\nwhat is the rate of change?\nwhat is f(7)?

Answer

Explanation:

Step1: Recall rate - of - change formula

The rate of change (slope) $m$ for a linear function is given by $m=\frac{\Delta y}{\Delta x}=\frac{f(x_2)-f(x_1)}{x_2 - x_1}$. Let $(x_1,f(x_1))=(3,-4)$ and $(x_2,f(x_2))=(5,-6)$.

Step2: Substitute values into formula

$m=\frac{-6-(-4)}{5 - 3}=\frac{-6 + 4}{2}=\frac{-2}{2}=-1$.

Step3: Find f(7) from table

From the table, when $x = 7$, $f(7)=-8$.

Answer:

The rate of change is - 1. $f(7)=-8$