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

Answer: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