An example of a wrong function equation is f(x) = sqrt(x) for all non-negative x.
Yes, a function can become an equation when it is set equal to a value or another expression. For example, if you have a function ( f(x) = 2x + 3 ), you can create an equation by setting it equal to a number, such as ( 2x + 3 = 7 ). This transforms the function into an equation that can be solved for the variable ( x ).
If a graph is a function, it will always have y=... or x=... (or anoher letter equals an equation) for example y= 3x-12 is a function
The equation x=c where c is a constant is the equation of a vertical line. It can't be a function but it is linear so the answer is no. For example, the vertical line produced by the linear equation x = 3 does not represent a function. We cannot write this equation so that y is a function of x because the only x-value is 3 and this "maps" to every real-number y.
This depends on the type of equation. Example: y=2x +2 is called a linear function. in the form of a binomial. y= 2x^2 +3x +2 =is a quadratic function. in the form of a trinomial.
An ordinary differential equation is an equation relating the derivatives of a function to the function and the variable being differentiated against. For example, dy/dx=y+x would be an ordinary differential equation. This is as opposed to a partial differential equation which relates the partial derivatives of a function to the partial variables such as d²u/dx²=-d²u/dt². In a linear ordinary differential equation, the various derivatives never get multiplied together, but they can get multiplied by the variable. For example, d²y/dx²+x*dy/dx=x would be a linear ordinary differential equation. A nonlinear ordinary differential equation does not have this restriction and lets you chain as many derivatives together as you want. For example, d²y/dx² * dy/dx * y = x would be a perfectly valid example
No. A function need not be linear. For example, y = sin(x) is a function of x but it is not a linear equation.
An example of a wave function is the Schrdinger equation in quantum mechanics, which describes the behavior of particles as both particles and waves.
If it is a linear function, it is quite easy to solve the equation explicitly, using standard methods of equation-solving. For example, if you have "y" as a function of "x", you would have to solve the variable for "x".
If a graph is a function, it will always have y=... or x=... (or anoher letter equals an equation) for example y= 3x-12 is a function
I don't think there is a special name for that. Note that not all functions can be described by a single equation - at least, not in a natural way. For example, a function may be described by parts.
To show that a wave function is a solution to the time-independent Schrödinger equation for a simple harmonic oscillator, you substitute the wave function into the Schrödinger equation and simplify. This will involve applying the Hamiltonian operator to the wave function and confirming that it equals a constant times the wave function.
You can tell if an equation is a function if for any x value that you put into the function, you get only one y value. The equation you asked about is the equation of a line. It is a function.
The equation x=c where c is a constant is the equation of a vertical line. It can't be a function but it is linear so the answer is no. For example, the vertical line produced by the linear equation x = 3 does not represent a function. We cannot write this equation so that y is a function of x because the only x-value is 3 and this "maps" to every real-number y.
This depends on the type of equation. Example: y=2x +2 is called a linear function. in the form of a binomial. y= 2x^2 +3x +2 =is a quadratic function. in the form of a trinomial.
An ordinary differential equation is an equation relating the derivatives of a function to the function and the variable being differentiated against. For example, dy/dx=y+x would be an ordinary differential equation. This is as opposed to a partial differential equation which relates the partial derivatives of a function to the partial variables such as d²u/dx²=-d²u/dt². In a linear ordinary differential equation, the various derivatives never get multiplied together, but they can get multiplied by the variable. For example, d²y/dx²+x*dy/dx=x would be a linear ordinary differential equation. A nonlinear ordinary differential equation does not have this restriction and lets you chain as many derivatives together as you want. For example, d²y/dx² * dy/dx * y = x would be a perfectly valid example
a function rule
The function of the conscience is to signal your brain when something is wrong. For example, if you are contemplating stealing a candy bar, your conscience should be telling you this is wrong.