Find the domain of each rational expression. f(x)=5x-7/4
2 answers:
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The two limits when x tends to zero are:
Notice that we have a jump at x = 0.
Then we can take two limits, one going from the negative side (where we will go along the blue line)
And other from the positive side (where we go along the orange line).
We will get:
Notice that the two limits are different, that means that the function is not a continuous function.
If you want to learn more about limits:
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Answer:
= Irrational
43.95 (repeat sign) = Rational
-3π = Irrational
-√49 = Rational
6/15 = Rational
Step-by-step explanation:
Note:
A rational number can be defined as any number that can be expressed or written in the p/q form, where 'p' and 'q' are integers and q is a non-zero number. An irrational number on the other hand cannot be expressed in p/q form and the decimal expansion of an irrational number is non-repeating and non-terminating.
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The square root of a negative number is imaginary.
Natural Number Test
A number is natural if it is one of the counting numbers (greater than 0), i.e., 1,2,3,4,5,...
Since NAN is not both positive and a counting number, NAN is not a natural number
Whole Number Test:
Whole Numbers are positive numbers, including 0, with no decimal or fractional parts
Since NAN is not both ≥ 0 and an integer, NAN is a not a whole number
Integer Test
The number is an integer if it is a whole number (no fractions or decimals) positive or negative including the number 0, ...,-5,-4,-3,-2,-1,0,1,2,3,4,5,...
Since NAN is not a positive or negative number (no decimals or fractions), NAN is not an integer
Rational Number Test
The number NAN is rational if it is an integer or decimal
A rational number is a number that can be represented a/b where a and b are integers and b is not equal to 0.
Irrational Number Test:
An irrational number is a number that cannot be expressed as a ratio between two integers and is not an imaginary number.
Since NAN is the square root of a negative number, it is imaginary
Imaginary Numbers are not rational
Imaginary
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43.95 ⇒ With repeat sign over 43.95
The decimal places repeat an infinite amount of times and when a decimal repeats it's rational.
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Pi is a Greek letter (π), and one of the most well-known mathematical constants.
It is the ratio of a circle's circumference to its diameter which is always constant.
pi (π) approximately equals 3.14159265359... and is a non-terminating non-repeating decimal number.
Hence 'pi' is an irrational number.
Any number with pi is considered irrational.
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The square root of a negative number is imaginary.
Natural Number Test
A number is natural if it is one of the counting numbers (greater than 0), i.e., 1,2,3,4,5,...
Since NAN is not both positive and a counting number, NAN is not a natural number
Whole Number Test:
Whole Numbers are positive numbers, including 0, with no decimal or fractional parts
Since NAN is not both ≥ 0 and an integer, NAN is a not a whole number
Integer Test
The number is an integer if it is a whole number (no fractions or decimals) positive or negative including the number 0, ...,-5,-4,-3,-2,-1,0,1,2,3,4,5,...
Since NAN is not a positive or negative number (no decimals or fractions), NAN is not an integer
Rational Number Test
The number NAN is rational if it is an integer or decimal
A rational number is a number that can be represented a/b where a and b are integers and b is not equal to 0.
Irrational Number Test:
An irrational number is a number that cannot be expressed as a ratio between two integers and is not an imaginary number.
Since NAN is the square root of a negative number, it is imaginary
Imaginary Numbers are not rational
Imaginary
But is rational as it equals -7.
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Rational because the decimal terminates:
6/15 = 0.4/0.40...