What do all linear functions of the form f(x) = ax + a, a > 0, have in common?

SOLUTION

Given linear function: \(f(x) = ax + a = a(x + 1), a>0\)
For any \(a, f(−1) = a(−1 + 1) = a(0) = 0\)
So all such lines pass through (\(−1,0\)) on the \(x-\)axis.

Concept Note

Lines of the form \(f(x) = a(x + 1)\) have a fixed \(x-\)intercept at \(x = −1\), while the \(y-\)intercept varies with \(a\).