Question

Diagram 1 shows absolute function of f(x)= 3x-1a)State the domain for that functionb)State the value of a

Answer 1

The function given is,

$f(x)=3x-1$

a) Domain

This is the set of all points over which a function is defined.

Therefore, the domain of the function is

$-2\leq x\leq1$

b) Solving for the value of a

To solve for the value of a, the value of y = 0 at x = a

Therefore,

$\begin{gathered} f(x)=3x-1 \\ \text{where,} \\ f(x)=y=0 \\ x=a \end{gathered}$

Solving for a

$\begin{gathered} 0=3(a)-1 \\ 0=3a-1 \\ \end{gathered}$

Collect like terms

$\begin{gathered} 3a=0+1 \\ 3a=1 \end{gathered}$

Divide both sides by 3

$\begin{gathered} \frac{3a}{3}=\frac{1}{3} \\ a=\frac{1}{3} \end{gathered}$

Hence,

$a=\frac{1}{3}$