Answer:
To find a linear function that satisfies the given conditions, we can use the slope-intercept form of a linear equation, which is given by:
f(x) = mx + b
where m represents the slope of the line and b represents the y-intercept.
Given that f(0) = 2, we can substitute x = 0 into the equation to find the value of b:
f(0) = m(0) + b
2 = 0 + b
b = 2
Now, we have the value of b. Next, we need to find the value of m using the second condition f(2) = 4:
f(2) = m(2) + 2
4 = 2m + 2
2m = 4 - 2
2m = 2
m = 1
Therefore, the linear function that satisfies f(0) = 2 and f(2) = 4 is:
f(x) = x + 2
This function represents a line with a slope of 1 and a y-intercept of 2. As x increases by 1, y also increases by 1.
Explanation: