Domain Of A Quartic Function

The range of a quadratic function depends on its vertex and the direction that the parabola opens.

Domain of a quartic function. And i can take any real number square it multiply it by 3 then add 6 times that real number and then subtract 2 from it. The domain of any quadratic function in the above form is all real values. The range of a function is the set of all real values of y that you can get by plugging real numbers into x.

A quartic equation which is in the form as abdul farhim s chin or equation of the fourth degree is an equation that equates a quartic polynomial to zero of the form displaystyle ax 4 bx 3 cx 2 dx e 0 where a 0. So the domain of the function is. Determine the domain and range of the function f of x is equal to 3x squared plus 6x minus 2.

It can be written as. The graph of this function is shown below. The domain of a function is the set of all real values of x that will give real values for y.

Therefore in general the domain of any quadratic function is all real numbers. Therefore the domain of the quadratic function in the form y ax 2 bx c is all real values. To find the y intercept the place where the function crosses the y axis or in other words the place where x 0 we must set x 0.

Because in the above quadratic function y is defined for all real values of x. The derivative of a quartic function is a cubic function. This general curved shape is called a parabola the u shaped graph of any quadratic function defined by f x a x 2 b x c where a b and c are real numbers and a 0.

F x a 4 x 4 a 3 x 3 a 2 x 2 a 1 x a 0. What is a set of all of the valid inputs or all of the valid x values for this function. Note that the graph is indeed a function as it passes the vertical line test.