Answer:
A function is increasing when the gradient is positive
A function is decreasing when the gradient is negative
<u>Question 7</u>
If you draw a tangent to the curve in the interval x < -2 then the tangent will have a positive gradient, and so the function is increasing in this interval.
If you draw a tangent to the curve in the interval x > -2 then the tangent will have a negative gradient, and so the function is decreasing in this interval.
If you draw a tangent to the curve at the vertex of the parabola, it will be a horizontal line, and so the gradient at x = -2 will be zero.
The function is increasing when x < -2
The function is decreasing when x > -2
<u>Additional information</u>
We can actually determine the intervals where the function is increasing and decreasing by differentiating the function.
The equation of this graph is:
The function is increasing when
The function is decreasing when
This concurs with the observations made from the graph.
<u>Question 8</u>
This is a straight line graph. The gradient is negative, so:
The function is decreasing for all real values of x
But if they want the interval for the grid only, it would be -4 ≤ x ≤ 1
<u>Question 9</u>
If you draw a tangent to the curve in the interval x < -1 then the tangent will have a negative gradient, and so the function is decreasing in this interval.
If you draw a tangent to the curve in the interval x > -1 then the tangent will have a positive gradient, and so the function is increasing in this interval.
If you draw a tangent to the curve at the vertex of the parabola, it will be a horizontal line, and so the gradient at x = -1 will be zero.
The function is decreasing when x < -1
The function is increasing when x > -1