When you plot a function with asymptotes, you know that the graph cannot cross the asymptotes, because the function cannot be valid at the asymptote. (Since that is the point of having an asymptotes - it is a "disconnect" where the function is not valid - e.g when dividing by zero or something equally strange would occur). So if you graph is crossing an asymptote at any point, something's gone wrong.
The domain. The independent variable. The x values in a function or two variable equation. Normally, the numbers on the horizontal axis represent the data you start with to figure out what will happen when you apply a function to those numbers. In a linear equation, y=3x+2 will cross the horizontal axis at (-2/3, 0), and will cross the vertical axis at (0,2), creating a line that moves upward to the right as the values on the horizontal axis increase.
It is a rectangle which is similar to the base.
The vertical cross sections are trapezia or triangles. The horizontal cross sections are rectangles which are mathematically similar to the base.
Circle
rectangle
The graph of an exponential function f(x) = bx approaches, but does not cross the x-axis. The x-axis is a horizontal asymptote.
Yes.
When graphing functions, an inverse function will be symmetric to the original function about the line y = x. Since a constant function is simply a straight, horizontal line, its inverse would be a straight, vertical line. However, a vertical line is not a function. Therefore, constant functions do not have inverse functions. Another way of figuring this question can be achieved using the horizontal line test. Look at your original function on a graph. If any horizontal line intersects the graph of the original function more than once, the original function does not have an inverse. The constant function is a horizontal line. Under the assumptions of the horizontal line test, a horizontal line infinitely will cross the original function. Thus, the constant function does not have an inverse function.
Horizontal line test is used for the determination of a function,if the horizontal line passes through one point of the given graph then it is a function and if it passes through more than one point then it will not a function. * * * * * No! It is a vertical line test. Consider the graph of y = sin(x): a horizontal line line will cross it twice in every 360 degrees! Convince me that y = sin(x) is not a function.
The domain. The independent variable. The x values in a function or two variable equation. Normally, the numbers on the horizontal axis represent the data you start with to figure out what will happen when you apply a function to those numbers. In a linear equation, y=3x+2 will cross the horizontal axis at (-2/3, 0), and will cross the vertical axis at (0,2), creating a line that moves upward to the right as the values on the horizontal axis increase.
It is a rectangle which is similar to the base.
The vertical cross sections are trapezia or triangles. The horizontal cross sections are rectangles which are mathematically similar to the base.
If the cylinder is standing on its flat face, the horizontal cross section is a circle. Otherwise, it is a line or a rectangle.
Circle
rectangle
A circle
a square