CPM Homework Banner

Home > CCA2 > Chapter 5 > Lesson 5.2.5 > Problem 5-113

5-113.

For functions of the form f(x) = mx, it is true that f(a) + f(b) = f(a + b). For example, when f(x) = 5x, f(a) + f(b) = 5a + 5b = 5(a + b) and f(a + b) = 5(a + b). Is f(a) + f(b) = f(a + b) true for all linear functions? Explain why or show why not. Homework Help ✎

Think of a linear function that has a y-intercept other than 0 and use it to check the relationship f(a) + f(b) = f(a + b).

For example, try the linear function f(x) = 2x + 3 (you should think of a different one for your own answer).

f(a) + f(b) = (2a + 3) + (2b + 3)
f(a + b) = 2(a + b) + 3
f(a) + f(b) = 2a + 2b + 6

But, 2a + 2b + 6 ≠ 2a + 2b + 3

f(a) + f(b) = f(a + b) is not true for all linear functions.