Describe and correct the error a student made in finding the interval(s) over which the function is positive and negative

The interval over which the function is positive is (-1 , 3)

The interval over which the function is negative is (-∞ , -1)∪(3 , ∞)

Step-by-step explanation:

* Lets explain the meaning of The intervals of positive and negative

 values of a function

- Interval of positive values means the values of x when the values

 of y are positive

- Y is positive means the graph is above the x-axis

- Interval of negative values means the values of x when the values

 of y are negative

- Y is negative means the graph is below the x-axis

- Remember that the value of y on the x-axis is zero, then the points

 of intersection between the graph and x-axis have zero value of y

 and zero is not positive nor negative, then the x-coordinate of

 these points do not belong to the intervals of positive or negative

* Lets solve the problem

∵ The graph represents a downward parabola

∵ The positive value of the parabola is above the x-axis

∵ The parabola intersects the x-axis at -1 , 3

∴ Y is positive at ⇒ -1 < x < 3

# -1 , 3 ∉ to the interval

∴ The interval over which the function is positive is (-1 , 3)

∵ The negative value of the parabola is below the x-axis

∵ The parabola intersects the x-axis at -1 , 3

∴ Y is negative at ⇒ -∞ < x < -1 and 3 < x < ∞

# -1 , 3 ∉ to the interval

∴ The interval over which the function is negative is (-∞ , -1)∪(3 , ∞)

* The error of the student he wrote Positive: [-1 , 3] which means

  that -1 , 3 ∈ to the intervals over positive

  which the function is positive or negative

what is the original number? you forgot to add it.

(0,,,0)

step-by-step explanation:

the table of x and y values is shown in the attached pic(part of question)

we have to decide according that graph

given points are (0, 0) (–1, 0), (2, 0)

when we graph these points on graph they show an increasing line as shown in the attached pic