Question

Write a linear function f with f(0) equals 2 and f(2) equals 4.

a. f(x) equals 2x
b. f(x) equals 2x plus 2
c. f(x) equals x plus 2
d. f(x) equals x

Answer 1

To find the linear function that goes through the points (0, 2) and (2, 4), calculate the slope which is 1, and use the y-intercept which is 2. The correct linear function is f(x) = x + 2, which is option c.

Step-by-step explanation:

To write a linear function f with f(0) = 2 and f(2) = 4, we need to determine the slope and y-intercept for the line. The slope, m, is the change in y divided by the change in x.

Here, the slope is (4 - 2) / (2 - 0) = 2 / 2 = 1. The y-intercept, b, is the value of f(x) when x is 0, which is given as 2. Thus, the equation of the line is f(x) = x + 2.

The correct option is c. f(x) = x + 2 because it satisfies both given points: f(0) = 2 and f(2) = 4.