Question

5. Sketch a graph and identify key features. f(x)=(3x+1)/x-3. find where f(x) > 0 and f(x) < 0 i only need to know f(x) > 0 and < 0

Answer 1

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

`f(x)=((3x+1))/(x-3)`

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

`\begin{gathered} f(x)=((3x+1))/(x-3)=0 \\ 3x+1=0 \\ 3x=-1 \\ x=-(1)/(3) \end{gathered}`

f(x) > 0,

`(-\infty,-(1)/(3)\rbrack\cup(3,\infty)`

First, we reeplace x = 0, to find the intercept in the y-axis

`f(0)=(3\cdot0+1)/(0-3)=-(1)/(3)`

f(x) < 0,

`(0,3)`