Discussion 1 Week 1 Algebra Essay Example
Explain in your own words what the meaning of domain is. Also, explain why a denominator cannot be zero?
The domain is a set of all real numbers used in place of a variable to assist in the functionality of the equation. It must exclude any real number that causes the denominator to be zero. A denominator cannot be zero because we must divide the denominator with the numerator and you cannot divide by zero. This means the value is undefined.
In my first expression, since the first letter in my first name starts with a T, I am going to use the following expression below:
1 - x² x Rational Expression
(1-x) (1+x) x each set contains terms that are perfect squares. Factor using the difference of squares formula: a²-b²= (a-b) (a+b).
(-x+1) (x+1) x Reorder polynomial left to right starting with highest order term. x=0 the domain of an expression is all real numbers except when the expression is undefined. x≠0 final answer undefined written in set notation. D={x|x ∈ R, x ≠ 0}
My second expression below:
2b – 2
2b² - 8 Rational expression
2 (b) + 2 (-1) 2b² - 8 Factor out GCF of 2 from each term.
2 (b-1)
2b² -8 Factor GCF 2 from 2b-2. 2 (b – 1)
2 (b²) + 2 (-4) Factor out GCF 2 from each term.
2 (b – 1)
2 (b² - 4) Factor out GCF 2 from 2b – 8.
2 (b -1)
2 (b-2) (b+2) each set contains terms that are perfect squares. Factor using the difference of squares formula: a²-b²= (a-b) (a+b).
2(b-2) (b+2) = 0 all of these are undefined and not part of the domain.
B=2,-2
The domain is a set of all real numbers used in place of a variable to assist in the functionality of the equation. It must exclude any real number that causes the denominator to be zero. A denominator cannot be zero because we must divide the denominator with the numerator and you cannot divide by zero. This means the value is undefined.
In my first expression, since the first letter in my first name starts with a T, I am going to use the following expression below:
1 - x² x Rational Expression
(1-x) (1+x) x each set contains terms that are perfect squares. Factor using the difference of squares formula: a²-b²= (a-b) (a+b).
(-x+1) (x+1) x Reorder polynomial left to right starting with highest order term. x=0 the domain of an expression is all real numbers except when the expression is undefined. x≠0 final answer undefined written in set notation. D={x|x ∈ R, x ≠ 0}
My second expression below:
2b – 2
2b² - 8 Rational expression
2 (b) + 2 (-1) 2b² - 8 Factor out GCF of 2 from each term.
2 (b-1)
2b² -8 Factor GCF 2 from 2b-2. 2 (b – 1)
2 (b²) + 2 (-4) Factor out GCF 2 from each term.
2 (b – 1)
2 (b² - 4) Factor out GCF 2 from 2b – 8.
2 (b -1)
2 (b-2) (b+2) each set contains terms that are perfect squares. Factor using the difference of squares formula: a²-b²= (a-b) (a+b).
2(b-2) (b+2) = 0 all of these are undefined and not part of the domain.
B=2,-2