Final answer:
By using the given values f₀=2 and f₂=4, we calculate the slope m and determine the y-intercept b to write the linear function f(x) = x + 2.
Step-by-step explanation:
To write a linear function given two values, we can use the slope-intercept form of a line, which is f(x) = mx + b. We are given f0 = 2, which means when x = 0, f(x) is 2; thus b = 2 because b represents the y-intercept. We are also given f2 = 4, meaning when x = 2, f(x) is 4.
To find the slope m, we use the change in y over the change in x: m = (f(x2) - f(x1)) / (x2 - x1). Substituting the given values in, we get m = (4 - 2) / (2 - 0) = 2 / 2 = 1. Now that we have both m and b, we can write the function: f(x) = x + 2.