Itβs vertex is not at the origin
Its vertex is not at the origin
vertex
Yes, if the range is the non-negative reals.
Both the Greatest Integer Function and the Absolute Value Function are considered Piece-Wise Defined Functions. This implies that the function was put together using parts from other functions.
Itβs vertex is not at the origin
Its vertex is not at the origin
In math a normal absolute value equations share a vertex.
y = 1/x
vertex
apex what is the range of the absolute... answer is nonnegative real num...
Yes. (I would like to note that I am not incredibly familiar with this so if someone with more knowledge on the subject wouldn't mind verifying this that would be great.)
A piecewise function is a function defined by two or more equations. A step functions is a piecewise function defined by a constant value over each part of its domain. You can write absolute value functions and step functions as piecewise functions so they're easier to graph.
There are three main types of vertices for an absolute value function. There are some vertices which are carried over from the function, and taking its absolute value makes no difference. For example, the vertex of the parabola y = 3*x^2 + 15 is not affected by taking absolute values. Then there are some vertices which are reflected in the x-axis because of the absolute value. For example, the vertex of the absolute value of y = 3*x^2 - 15, that is y = |3*x^2 - 15| will be the reflection of the vertex of the original. Finally there are points where the function is "bounced" off the x-axis. These points can be identified by solving for the roots of the original equation. -------------- The above answer considers the absolute value of a parabola. There is a simpler, more common function, y = lxl. In this form, the vertex is (0,0). A more general form is y = lx-hl +k, where y = lxl has been translated h units to the right and k units up. This function has its vertex at (h,k). Finally, for y = albx-hl + k, where the graph has been stretched vertically by a factor of a and compressed horizontally by a factor of b, the vertex will be at (h/b,ak). Of course, you can always find the vertex by graphing, especially since you might not remember the 2nd or 3rd parts above.
Linear
the range is all real numbers
apex what is the range of the absolute... answer is nonnegative real num...