The intervals in which graph of the function is positive are [tex]\boxed{\left( { - \infty , - 1} \right)}{\text{ and }}\boxed{\left( {2.5,\infty } \right)}[/tex] and intervals in which graph of the function is negative is [tex]\boxed{\left[ { - 1,2.5} \right]}.[/tex]
Further explanation:
Explanation:
The linear equation with slope m and y-intercept c is given as follows.
[tex]\boxed{y = mx + c}[/tex]
The formula for slope of line with points [tex]\left( {{x_1},{y_1}} \right) {\text{and} \left( {{x_2},{y_2}} \right)[/tex] can be expressed as,
[tex]\boxed{m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}}[/tex]
If the slope is greater than zero then the graph is increasing.
[tex]m> 0[/tex]
If the slope is less than zero then the graph is decreasing.
[tex]m< 0[/tex]
From the graph it has been observed that the graph slope of the function is greater than zero in interval [tex]\left( { - \infty , - 1} \right)[/tex]. Hence, the function is increases.
From the graph it has been observed that the graph slope of the function is less than zero in interval [tex]\left[ { - 1,2.5} \right].[/tex] Hence, the function is decreasing.
From the graph it has been observed that the graph slope of the function is greater than zero in interval [tex]\left( {2.5,\infty } \right)[/tex]. Hence, the function is increases.
The intervals in which graph of the function is positive are [tex]\boxed{\left( { - \infty , - 1} \right)}{\text{ and }}\boxed{\left( {2.5,\infty } \right)}[/tex] and intervals in which graph of the function is negative is [tex]\boxed{\left[ { - 1,2.5} \right]}.[/tex]
Learn more:
- Learn more about inverse of the functionhttps://brainly.com/question/1632445.
- Learn more about equation of circle brainly.com/question/1506955.
- Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Linear equation
Keywords: Slope, intercept, y- intercept, x- intercept, points, function, relation, graph, increasing, decreasing, strictly increasing, strictly decreases, interval, graph grows, positive, negative.
