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What rational functions will have a hole at x2?
A rational function is undefined - you might say that it "has a hole" - at any point where the denominator is zero. Assuming you mean "... hole at x = 2", any rational function which has the factor (x-2) in its denominator will have a hole at x = 2.
Is 0.757575 rational or irrational?
The number 0.757575 is a rational number. A rational number is any number that can be expressed as a fraction where the numerator and denominator are integers and the denominator is not zero. In this case, 0.757575 can be expressed as the fraction 75/99, which meets the criteria for a rational number.
A rational expression is undefined whenever its denominator is zero?
False
Is 15.77 a rational or irrational number?
15.77 is a rational number. A rational number is any number that can be expressed as a fraction where the numerator and denominator are integers and the denominator is not zero. In this case, 15.77 can be written as 1577/100, which meets the criteria for a rational number.
Is 7 over 8 a rational number or irrational number?
7 over 8, which can be written as 7/8, is a rational number. A rational number is any number that can be expressed as a fraction where the numerator and denominator are integers, and the denominator is not zero. Since 7 and 8 are both integers, and 8 is not zero, 7/8 is a rational number.
What is called when the denominator is zero in a rational function?
The function is not defined at any values at which the denominator is zero.
Why can't the denominators of rational expressions be zero How can we find the domain of a rational function?
Rational expressions are fractions and are therefore undefined if the denominator is zero; the domain of a rational function is all real numbers except those that make the denominator of the related rational expression equal to 0. If a denominator contains variables, set it equal to zero and solve.
Why do we set the denominator to zero to graph a rational function?
We set the denominator to zero to find the singularities: points where the graph is undefined.
How do you find the domain of a rational function?
The domain of a rational function is the whole of the real numbers except those points where the denominator of the rational function, simplified if possible, is zero.
In rational functions what happens when w gets close to zero?
The answer depends on what w represents. If w is the denominator of the rational function then as w gets close to zero, the rational function tends toward plus or minus infinity - depending on the signs of the dominant terms in the numerator and denominator.
What can cause a rational function to be undefined at particular values of x?
A rational function can be undefined at particular values of ( x ) when the denominator equals zero, as division by zero is undefined in mathematics. This typically occurs at specific values of ( x ) that make the denominator a zero polynomial. Identifying these values is essential for understanding the function's domain and any potential discontinuities.
What is a rational function?
In mathematics, a rational function is any function which can be written as the ratio of two polynomial functions. Neither the coefficients of the polynomials nor the values taken by the function are necessarily rational numbers.In the case of one variable, , a function is called a rational function if and only if it can be written in the formwhere and are polynomial functions in and is not the zero polynomial. The domain of is the set of all points for which the denominator is not zero, where one assumes that the fraction is written in its lower degree terms, that is, and have several factors of the positive degree.Every polynomial function is a rational function with . A function that cannot be written in this form (for example, ) is not a rational function (but the adjective "irrational" is not generally used for functions, but only for numbers).An expression of the form is called a rational expression. The need not be a variable. In abstract algebra the is called an indeterminate.A rational equation is an equation in which two rational expressions are set equal to each other. These expressions obey the same rules as fractions. The equations can be solved by cross-multiplying. Division by zero is undefined, so that a solution causing formal division by zero is rejected.
What rational functions will have a hole at x2?
A rational function is undefined - you might say that it "has a hole" - at any point where the denominator is zero. Assuming you mean "... hole at x = 2", any rational function which has the factor (x-2) in its denominator will have a hole at x = 2.
Do all rational functions have holes?
Not all rational functions have holes. A rational function is a ratio of two polynomials, and holes occur at points where both the numerator and denominator equal zero, indicating a common factor. If a rational function has no common factors between the numerator and denominator, it will not have any holes, although it may have vertical asymptotes or other features.
Is zero over an integer denominator always rational?
Yes
What can the denominator of a rational expression never equal?
It cannot be zero.
A rational expression is undefined whenever its denominator is zero-?
True
