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

Answer 1

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: