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How do you write 4sin6xcos6x as a function of a single variable?
4 sin(6x) cos(6x) is already a function of a single variable. The variable is ' x '.
What is the function definition?
function is the relationship between independent variable & dependent variable i.e. F:R-R
What is a derivative of inspired?
Inspired could be though of as an integer as it does not have an exponent. d/dx(inspired) = 0 ==== Or, as a variable with the implied exponent 1. Using the power rule. d/dx(inspired 1 - 1) = inspired0 = 1 ====
How do you identify the range of a function?
The range of a function is the interval (or intervals) over which the independent variable is valid, i.e. results in a valid value of the function.
How do you change an exponential functions to a logarithmic function?
If y is an exponential function of x then x is a logarithmic function of y - so to change from an exponential function to a logarithmic function, change the subject of the function from one variable to the other.
What is unique about the linear function?
Each variable has an exponent equal to one.
What is a nonlinear relationship?
In mathematics, when the dependent variable is not proportional to the independent variable. The function does not vary directly with the input. Example: y=sin (x).
What one thing in this function tells you it will be nonlinear?
The presence of any term that is not a constant or a multiple of the independent variable. It can be any other power of that variable, or a trigonometric or exponential or any other function.
What is meaning of exponent with variable?
That you have an exponential function. These functions are typical for certain practical problems, such as population growth, or radioactive decay (with a negative exponent in this case).
How can you determine if a function is a quadratic function from its equation?
If the highest exponent of independent variable(say x) is 2 and the highest exponent of dependent variable(say y) is 1 and x and y are not multiplied, then the function is quadratic. For example: 3x-y+x2= 2y-5x+7 represents a quadratic function but y= xy+x2+5 doesn't represent a quadratic function.
How can you tell by looking only at the equation of a function with no graph that it is nonlinear?
To be linear, there should only be constants, and variables with constant coefficients. No powers of variables, or numbers raised to the power of a variable, or any other nonlinear function such as log, ln, sin, cos, tan, cosh, etc.
In exponential growth functions the base of the exponent must be greater than 1. How would the function change if the base of the exponent were 1 How would the function change if the base of the expon?
"The base of the exponent" doesn't make sense; base and exponent are two different parts of an exponential function. To be an exponential function, the variable must be in the exponent. Assuming the base is positive:* If the base is greater than 1, the function increases. * If the base is 1, you have a constant function. * If the base is less than 1, the function decreases.
Intricate examples of nonlinear function?
Here is a simple example of a nonlinear function. Y = X2 =====Build on that!
True or false In a nonlinear equation each variable must only have one solution?
In a nonlinear equation, each variable must only have one solution.
Degree of a term?
the variable's exponent
Can a polynomial have a variable exponent?
No. An expression can have a variable exponent (for instance, 2 to the power x, or x to the power y), but that is no longer a polynomial.
What is a non-linear equation?
A nonlinear equation does not produce a straight line and the exponent is to the second power or more. x square plus 3y =5 is an example of a nonlinear equation.
