Question

Consider the table of values below.

x = 0 1 2 3
f(x) = 8 6 4 2
Find the linear function f(x).
A. f(x) = -x + 8
B. f(x) = -2x + 3
C. f(x) = 2x + 8
D. f(x) = -2x + 13
E. f(x) = -2x + 8
F. f(x) = 8x - 2

Answer 1

The linear function that matches the table of values given is f(x) = -2x + 8.

Step-by-step explanation:

To find the linear function f(x) that matches the table of values given, we can use two points from the table to determine the slope (m) and then find the y-intercept (b) to write the equation in slope-intercept form (y = mx + b).

Looking at the points (0, 8) and (1, 6), we can calculate the slope as follows:

m = (f(1) - f(0)) / (1 - 0) = (6 - 8) / (1 - 0) = -2

Since we have a point (0, 8) and now know the slope is -2, our linear equation is:

f(x) = -2x + b

We can substitute the point (0, 8) into the equation to find b:

8 = -2(0) + b

b = 8

Therefore, the function is:

f(x) = -2x + 8