Chapter 3 - Linear and Quadratic Functions - 3.1 Properties of Linear Functions and Linear Models - 3.1 Assess Your Understanding - Page 129: 55

Odd: $b=0$. Even: $m=0$.

We know that if a function is odd, then $f(-x)=-f(x).$ We know that if a function is even, then $f(-x)=f(x).$ Hence we plug in $-x$ to see what happens. $f(-x)=-mx+b.$ If it is odd, then $-mx+b=-f(x)=-(mx+b)\\-mx+b=-mx-b\\b=-b\\2b=0\\b=0$ If it is even, then $-mx+b=f(x)=mx+b\\-mx+b=mx+b\\-mx=mx\\mx=0\\m=0.$