Answer:
f(x) > 0, for (-inf, -1/3] and (3, inf)
f(x) < 0, for (0, 3)
Step by step explanation:
The graph of the equation
[tex]f(x)=\frac{(3x+1)}{x-3}[/tex]
From looking at the graph we can say that:
First we find the value where the function f(x) = 0, to find the intercept in the x-axis
[tex]\begin{gathered} f(x)=\frac{(3x+1)}{x-3}=0 \\ 3x+1=0 \\ 3x=-1 \\ x=-\frac{1}{3} \end{gathered}[/tex]
f(x) > 0,
[tex](-\infty,-\frac{1}{3}\rbrack\cup(3,\infty)[/tex]
First, we reeplace x = 0, to find the intercept in the y-axis
[tex]f(0)=\frac{3\cdot0+1}{0-3}=-\frac{1}{3}[/tex]
f(x) < 0,
[tex](0,3)[/tex]
