### Home > A2C > Chapter 6 > Lesson 6.2.5 > Problem 6-114

6-114.

For functions of the form *f (x)* = *mx,* it is true that *f(a) + f(b)* = *f(a + b)*? For example, when *f(x)* = 5*x, f(a) + f(b) = *5*a + *5*b = *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*) = 2*x* + 3 (you should think of a different one for your own answer).

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

But, 2*a* + 2*b* + 6 ≠ 2*a* + 2*b* + 3

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