Answer:
The rule for the linear function in the table is f(x) = -4x.
Step-by-step explanation:
To find the rule of a linear function from a table, you need to first find the value of the slope, or the change in y-values ÷ the change in x - values. You can pick any two points on the table, as long as the x and f(x) are corresponding, and subtract them: (-16 - 0) ÷ (4-0) = -16 ÷ 4 = -4. -4 is the value of the slope and is connected to the x: -4x. The other part you need for your rule, is the value of f(x) when x = 0. Looking at the table, the value of f(x) when x = 0 is 0, so there is no need to add + 0 to your rule, leaving a final answer of f(x) = -4x.
