## Intermediate Algebra for College Students (7th Edition)

(a.) $f(x_1+x_2)=mx_1+mx_2+b$. (b.) $f(x_1)+f(x_2) = mx_1+mx_2+2b$. (c.) Not true
The given linear function is $f(x)=mx+b$ (a.) For $f(x_1+x_2)$ plug $x=x_1+x_2$ into the given function. $f(x_1+x_2)=m(x_1+x_2)+b$ $f(x_1+x_2)=mx_1+mx_2+b$ (b.) For $f(x_1)+f(x_2)$ plug $x=x_1$ and $x=x_2$ into the given function. $f(x_1)=mx_1+b$ and $f(x_2)=mx_2+b$ Add both equations. $f(x_1)+f(x_2) = mx_1+b+mx_2+b$ $f(x_1)+f(x_2) = mx_1+mx_2+2b$ (c.) From part (a.) and part (b.). $f(x_1+x_2)\neq f(x_1)+f(x_2)$