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What is the difference of odd and even functions?
An even function is symmetric about the y-axis. An odd function is anti-symmetric.
Does the graph of and odd function have to contain the origin?
No function ever really has to contain the origin if you constrain the domain to not include zero. Another way would be to just start graphing at x=1 and continue increasing x. In fact, you don't even have to graph at all since an odd function is defined as f(x) + f(-x) = 0
Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is even?
If the point (x,y) is on the graph of the even function y = f(x) then so is (-x,y)
How do you determine if a function is even or odd?
You can tell if a function is even or odd by looking at its graph. If a function has rotational symmetry about the origin (meaning it can be rotated 180 degrees about the origin and remain the same function) it is an odd function. f(-x)=-f(x) An example of an odd function is the parent sine function: y=sinx If a function has symmetry about the y-axis (meaning it can be reflected across the y-axis to produce the same image) it is an even function. f(x)=f(-x) An example of an even function is the parent quadratic function: y=x2
How do you tell if a function is even or odd?
You can tell if a function is even or odd by looking at its graph. If a function has rotational symmetry about the origin (meaning it can be rotated 180 degrees about the origin and remain the same function) it is an odd function. f(-x)=-f(x) An example of an odd function is the parent sine function: y=sinx If a function has symmetry about the y-axis (meaning it can be reflected across the y-axis to produce the same image) it is an even function. f(x)=f(-x) An example of an even function is the parent quadratic function: y=x2
How does the parity evenness oddness of a polynomial functions degree affect its graph?
An even function is symmetric about the y-axis. The graph to the left of the y-axis can be reflected onto the graph to the right. An odd function is anti-symmetric about the origin. The graph to the left of the y-axis must be reflected in the y-axis as well as in the x-axis (either one can be done first).
Is Y equals 0 an even or odd function?
f(x) = 0 is a constant function. This particular constant function is both even and odd. Requirements for an even function: f(x) = f(-x) Geometrically, the graph of an even function is symmetric with respect to the y-axis The graph of a constant function is a horizontal line and will be symmetric with respect to the y-axis. y=0 or f(x)=0 is a constant function which is symmetric with respect to the y-axis. Requirements for an odd function: -f(x) = f(-x) Geometrically, it is symmetric about the origin. While the constant function f(x)=0 is symmetric about the origin, constant function such as y=1 is not. and if we look at -f(x)=f(-x) for 1, we have -f(x)=-1 but f(-1)=1 since it is a constant function so y=1 is a constant function but not odd. So f(x)=c is odd if and only iff c=0 f(x)=0 is the only function which is both even and odd.
What is the difference of odd and even functions?
An even function is symmetric about the y-axis. An odd function is anti-symmetric.
What does even distribution mean?
It means that the probability density function is symmetric about 0.
Does the graph of and odd function have to contain the origin?
No function ever really has to contain the origin if you constrain the domain to not include zero. Another way would be to just start graphing at x=1 and continue increasing x. In fact, you don't even have to graph at all since an odd function is defined as f(x) + f(-x) = 0
Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is even?
If the point (x,y) is on the graph of the even function y = f(x) then so is (-x,y)
How do you determine if a function is even or odd?
You can tell if a function is even or odd by looking at its graph. If a function has rotational symmetry about the origin (meaning it can be rotated 180 degrees about the origin and remain the same function) it is an odd function. f(-x)=-f(x) An example of an odd function is the parent sine function: y=sinx If a function has symmetry about the y-axis (meaning it can be reflected across the y-axis to produce the same image) it is an even function. f(x)=f(-x) An example of an even function is the parent quadratic function: y=x2
How do you tell if a function is even or odd?
You can tell if a function is even or odd by looking at its graph. If a function has rotational symmetry about the origin (meaning it can be rotated 180 degrees about the origin and remain the same function) it is an odd function. f(-x)=-f(x) An example of an odd function is the parent sine function: y=sinx If a function has symmetry about the y-axis (meaning it can be reflected across the y-axis to produce the same image) it is an even function. f(x)=f(-x) An example of an even function is the parent quadratic function: y=x2
Why cosx is even function?
its graph is symetric x-axises
What kind of symmetry does an even function have?
A function f(x) is even if f(-x) = f(x). A graph of f(x) would be symmetric about the y-axis (vertical symmetry about x=0). f(x) need not be "well-behaved" or even continuous, unlike the examples given in Wikipedia article on "Even and odd functions". The article does make this clear - under "Some facts".
What is a function that is symmetric with respect to the y-axis?
A function that is symmetric with respect to the y-axis is an even function.A function f is an even function if f(-x) = f(x) for all x in the domain of f. that is that the right side of the equation does not change if x is replaced with -x. For example,f(x) = x^2f(-x) = (-x)^2 = x^2
What are even and odd functions?
An even function is a function that creates symmetry across the y-axis. An odd function is a function that creates origin symmetry.
