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What is the range of absolute value functions My teacher said it would be all real numbers. However I thought it would be positive real numbers. Can you explain who is right and why?
The absolute value of a number is positive, so the range is always a positive real number. You are correct. The domain, that is the value before you take the absolute value, is all real numbers, but the range is always positive.
What is an arithmetic function?
An arithmetic function is any function which is defined for all positive integers, and has values which are either real or complex.
Exmaple of real life absolute value function?
Time. Time cannot be negative, only positive.
How would you explain to a seventh grader the difference between the domains of an odd root radical function and an even root radical function?
To start with, when you multiply an even number of negative numbers, the answer is positive. When you multiply an odd number of negative numbers, the answer is negative. When you multiply any number of positive numbers, the answer is always positive. For positive numbers, the value of a power is always positive. For negative numbers, the value of an odd power is negative, and the value of an even power is positive. Finding roots is the inverse of taking powers, so that an odd-root function can be evaluated for any value of x. An even-root function, however, cannot be evaluated when the value of x is negative, since an even power can never result in a negative answer. The domain of an odd root function is all real numbers; the domain of an even root function is the non-negative real numbers.
How can you find th discriminate of a function?
Discriminant = b2 - 4ac A positive answer means two real roots, a 0 answer means one real root and a negative answer means no real roots. Example X2 + 3X - 10 = 0 a = 1 b = 3 c = -10 32 - 4(1)(- 10) = 49 ----------------a positive answer telling you this quadratic function has two real roots.
What is the domain of logarithm and exponential function?
Domain of the logarithm function is the positive real numbers. Domain of exponential function is the real numbers.
What is the range of absolute value functions My teacher said it would be all real numbers. However I thought it would be positive real numbers. Can you explain who is right and why?
The absolute value of a number is positive, so the range is always a positive real number. You are correct. The domain, that is the value before you take the absolute value, is all real numbers, but the range is always positive.
What is the range of an absolute value function?
the range is a positive real number
What is an arithmetic function?
An arithmetic function is any function which is defined for all positive integers, and has values which are either real or complex.
Why negative numbers don't have logarithim?
The logarithmic function is not defined for zero or negative numbers. Logarithms are the inverse of the exponential function for a positive base. Any exponent of a positive base must be positive. So the range of any exponential function is the positive real line. Consequently the domain of the the inverse function - the logarithm - is the positive real line. That is, logarithms are not defined for zero or negative numbers. (Wait until you get to complex analysis, though!)
Is the cube root of negative number a positive?
No, because the inverse function would not work. Every time you multiply a positive by a positive you get a positive.
Why can the value of tan equal any positive real number?
Because that is the way the tan function is defined!
Exmaple of real life absolute value function?
Time. Time cannot be negative, only positive.
How would you explain to a seventh grader the difference between the domains of an odd root radical function and an even root radical function?
To start with, when you multiply an even number of negative numbers, the answer is positive. When you multiply an odd number of negative numbers, the answer is negative. When you multiply any number of positive numbers, the answer is always positive. For positive numbers, the value of a power is always positive. For negative numbers, the value of an odd power is negative, and the value of an even power is positive. Finding roots is the inverse of taking powers, so that an odd-root function can be evaluated for any value of x. An even-root function, however, cannot be evaluated when the value of x is negative, since an even power can never result in a negative answer. The domain of an odd root function is all real numbers; the domain of an even root function is the non-negative real numbers.
The range of the function given below is the set of all positive real numbers less than 7?
false
How can you find th discriminate of a function?
Discriminant = b2 - 4ac A positive answer means two real roots, a 0 answer means one real root and a negative answer means no real roots. Example X2 + 3X - 10 = 0 a = 1 b = 3 c = -10 32 - 4(1)(- 10) = 49 ----------------a positive answer telling you this quadratic function has two real roots.
Could this ever be the rule of a function For input x the output is the number whose square is x If so what is its domain and range?
Yes, the domain(input) would be all natural numbers (numbers greater or equal to zero). The range (output) would be all real numbers. -- Not only natural numbers would be considered part of this domain, all negative numbers are also reasonable inputs to this function, as any negative number multiplied by itself would produce a positive number..... The output (range) would therefore be all positive real numbers......
