Question

What intervals would you use to determine where the function is positive and negative?

Answer 1

For this case we have a graph of a function$y = f (x)$ whose slope is given by:

$m =\frac{ f (x1) -f (x2)}{ x2-x1}$

When $m> 0$ the graph is increasing

When $m$the graph is decreasing

So:

• Interval (-∞, -1) slope $m> 0$, so the graph grows

• Interval [-1,2.5] the slope $m$, so the graph decreases

• Interval (2.5, ∞) slope $m> 0$, so the graph grows

Answer:

(-∞, -1) $f (x)> 0$

 [-1, 2.5] $f (x)$

(2.5, ∞) $f (x)> 0$

Answer 2

The intervals in which graph of the function is positive are $\boxed{\left( { - \infty , - 1} \right)}{\text{ and }}\boxed{\left( {2.5,\infty } \right)}$ and intervals in which graph of the function is negative is $\boxed{\left[ { - 1,2.5} \right]}.$

Further explanation:

Explanation:

The linear equation with slope m and y-intercept c is given as follows.

$\boxed{y = mx + c}$

The formula for slope of line with points $\left( {{x_1},{y_1}} \right) {\text{and} \left( {{x_2},{y_2}} \right)$ can be expressed as,

$\boxed{m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}}$

If the slope is greater than zero then the graph is increasing.

$m> 0$

If the slope is less than zero then the graph is decreasing.

$m< 0$

From the graph it has been observed that the graph slope of the function is greater than zero in interval $\left( { - \infty , - 1} \right)$. 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 $\left[ { - 1,2.5} \right].$ 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 $\left( {2.5,\infty } \right)$. Hence, the function is increases.

The intervals in which graph of the function is positive are $\boxed{\left( { - \infty , - 1} \right)}{\text{ and }}\boxed{\left( {2.5,\infty } \right)}$ and intervals in which graph of the function is negative is $\boxed{\left[ { - 1,2.5} \right]}.$

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function 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.