Chapter 2: Introduction to Linear Polynomials

Exercise

Question

Question: 14

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

Answer

1
Factorise f(x) to write it as a product.
$f(x) = ax + a = a(x + 1)$
2
Find the value of x for which f(x) = 0.
\text{${color:#2E2EFF}0{/color} = a(x + 1)$}
⇒
\text{ $0 = x + 1$ $\quad$ ${color:#625B5F}[Since a > 0, a is not 0; divide both sides by a]{/color}$}
⇒
\text{ $x = -1$ $\quad$ ${color:#625B5F}[Hence, all lines pass through (-1, 0), their common x-intercept.]{/color}$}
3
Write the common properties of all these linear functions.
Answer: All these lines pass through $(-1, 0)$, have the same $x$-intercept, and have a positive slope because $a > 0$.
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