Why is an ellipse, hyperbola, and circle not a function?
The vertical line test is a graphical way to show that for a graph of a function mapping one variable to another in the Cartesian plane. There is no reason why a function can't have any of …
Notation for piecewise equations with vertical lines
May 17, 2015 · Is there any notation that makes it possible to define a piecewise equation that contains one or more vertical lines? For instance, how would one attribute two lines $y=2x+1$ …
Difference between horizontal and vertical line tests.
If a horizontal line cuts the curve more than once at some point, then the curve doesn't have an inverse function. So in short, if you have a curve, the vertical line test checks if that curve is a …
How do I reflect a function about a specific line?
Reflecting a function along the line y = x is the same as computing the inverse of the function. So use a method for computing the inverse of a function to find the reflection about the line y = x.
Is the slope of a vertical line infinity or undefined?
A vertical line is not a function and it cannot have a derivative. If you describe the function of x with respect to y, then sure the derivative is $ {dx\over dy} = 0$.
Vertical Tangent line with Implicit Differentiation
Feb 23, 2015 · Vertical Tangent line with Implicit Differentiation Ask Question Asked 10 years, 8 months ago Modified 10 years, 8 months ago
How can a function have a vertical tangent and be continuous?
6 I read somewhere that, "a function with a vertical tangent may be continuous but not differentiable." Is this correct and, if so, what is an example of it? I can't think how a function …
What does the vertical bar mean in $ \\left.\\frac{\\partial f ...
Jun 13, 2015 · The vertical bar is often used to mean that we must insert the conditions in the expression. For partial derivatives my humble opinion is that we should not use it regularly. …
Why can a circle be described by an equation but not by a function?
Jan 22, 2015 · A function has to pass the "vertical line test." It can at most have one point at any vertical line.
calculus - How can a "proper" function have a vertical slope ...
Oct 5, 2019 · As I understand, in the graph I pasted we cannot take the derivative of x=0 because the slope is vertical, hence we cannot see the instantaneous rate of change of x to y as the y …