The following problem is a parabola so there is only one turning points so the answer is going to be: 2
No.
They cannot.
If the denominator is zero at some point, then the function is not defined at the corresponding points.
Yes, if no endpoints are defined.
The answer is all the points on the line defined by 25x - 12y = 1
No.
They cannot.
Yes. So long as the function has a value at the points in question, the function is considered defined.
If the denominator is zero at some point, then the function is not defined at the corresponding points.
Two.Two.Two.Two.
Differentiation, is often used to find the tangent of a curved graph. Each time you differentiate a function, you decrease the number of turning points in the graph, to a minimum of no turning points i.e. y = 3x. Differentiating to different orders is also used to find tangents, of tangents.
Yes, if no endpoints are defined.
The answer is all the points on the line defined by 25x - 12y = 1
That's how "function" is defined. If you have two points with the same x-coordinates, you have a "relation", but not a "function". A function is a special type of relation. The idea of a function is that, for every value of the independent variable (for example, "x"), the dependent variable (for example, "y") is uniquely defined. In other words, you can consider a function as a rule that assigns a y-value uniquely to every x-value.
A relation is an expression that is not a function. A function is defined as only having one domain per range, meaning that when graphed, a function will have no two points on the same vertical line. If your expression is graphed and two points do appear on the same vertical line, it is a relation, not a function.
{| |- | A line is defined by naming at least two points. It contains an infinite number of points, but two have to be identified. A line can also be defined by a single point and a direction. |}
What were the different turning points of Pearl Harbor?