Positive and Negativity of a Linear Function

Now, we will see an example in which we find the domain of positivity and negativity of the function by solving an inequality:

Let's see an example in which we find the domains of positivity and negativity of the function through a graph:

Let's observe the point of intersection of the function with the axis :$X$

Given the function: $y=4x-2$

What is the domain of positivity and what is the domain of negativity of the function?

Let's remember that when we are asked about the domain of positivity, we are asked in which values of $X$, the values of $Y$ are positive.

Therefore, when $Y>0$

We will take the equation equal to $Y$

$4X-2$

And check when it is greater than $0$

$4X-2>0$

We solve the inequality:

$4X>2$

$X>0.5$

The domain of positivity of the line is:

$X>0.5$

Now let's remember that when we are asked about the domain of negativity, we are asked in which values of $X$, the values of $Y$ are negative.

Therefore, when$Y<0$

We will take the equation equal to$Y$

$4X-2$

And check when it is less than $0$

$4X-2<0$

We solve the inequality:

$4X<2$

$X<0.5$

The domain of negativity of the line is:

$X<0.5$

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