Question

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

Answer 1

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