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To determine the value of ( C ) for which the function is one-to-one, we need to ensure that all output values are unique. The given outputs are ( 1, 2, 3, 5, 7, 11 ), and the output ( C ) must not equal any of these values. Therefore, ( C ) should be any value that is not ( 1, 2, 3, 5, 7, ) or ( 11 ) to maintain the one-to-one property.
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What is a function in which each y-value has only one corresponding x-value?
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Is x-1 a function?
Yes, ( x - 1 ) is a function. It represents a linear equation where each input value ( x ) corresponds to exactly one output value, calculated as ( x - 1 ). In mathematical terms, it can be expressed as ( f(x) = x - 1 ), which satisfies the definition of a function.
What does it mean for a function to be continuous?
It means that the function value doesn't make sudden jumps. For example, a function that rounds a number down to the closest integer is discontinuous for all integer values; for instance, when x changes from 0.99 to 1, or from 0.999999 to 1, or for any number arbitrarily close to 1 (but less than one) to one, the function value suddenly changes from 0 to 1. At other points, the function is continuous.
What is recursive function?
A recursive function is one in which the value of a function at each point depends on its value at one or more previous points. A rercursive function requires the first few values to be defined normally - these are called bases. Perhaps one of the most famous recursive function is the Fibonacci series, which has f(1) = 1 f(2) = 1 f(n) = f(n-1) + f(n-2) for n = 3, 4, 5, ... There are two bases and each subsequent value is defined in terms of the preceding two.
What do the absolute value of a function do to the graph of that function?
The absolute value of a function changes the original function by ensuring that any negative y values will in essence be positive. For instance, the function y = absolute value (x) will yield the value +1 when x equals -1. Graphically, this function will look like a "V".
What is a function in which each y-value has only one corresponding x-value?
-1
Is x-1 a function?
Yes, ( x - 1 ) is a function. It represents a linear equation where each input value ( x ) corresponds to exactly one output value, calculated as ( x - 1 ). In mathematical terms, it can be expressed as ( f(x) = x - 1 ), which satisfies the definition of a function.
What does it mean for a function to be continuous?
It means that the function value doesn't make sudden jumps. For example, a function that rounds a number down to the closest integer is discontinuous for all integer values; for instance, when x changes from 0.99 to 1, or from 0.999999 to 1, or for any number arbitrarily close to 1 (but less than one) to one, the function value suddenly changes from 0 to 1. At other points, the function is continuous.
What is recursive function?
A recursive function is one in which the value of a function at each point depends on its value at one or more previous points. A rercursive function requires the first few values to be defined normally - these are called bases. Perhaps one of the most famous recursive function is the Fibonacci series, which has f(1) = 1 f(2) = 1 f(n) = f(n-1) + f(n-2) for n = 3, 4, 5, ... There are two bases and each subsequent value is defined in terms of the preceding two.
Why sinθ value is less then and equal to one?
If you look at the definition of the sine function in a triangle, you'll discover that the maximum possible value of the sine function is ' 1 ' and the minimum possible value is ' -1 '. There's no angle that can have a sine greater than ' 1 ' or less than ' -1 '. So the absolute value of the sine of anything is always ' 1 ' or less.
What do the absolute value of a function do to the graph of that function?
The absolute value of a function changes the original function by ensuring that any negative y values will in essence be positive. For instance, the function y = absolute value (x) will yield the value +1 when x equals -1. Graphically, this function will look like a "V".
What is the maximum value that the graph of ycosx assume?
Both the function "cos x" and the function "sin x" have a maximum value of 1, and a minimum value of -1.
What value of a is required to normalize the function ?
To normalize a function, the value of a must be such that the integral of the function squared over its domain is equal to 1.
What is heaviside function?
The Heaviside function is a discontinuous step function. It is 0 for all values less than some specific value. At and after that value, it takes the value 1. The Heaviside function can be used to represent an "Off-On" function.See link for more.The Heaviside function is a discontinuous step function. It is 0 for all values less than some specific value. At and after that value, it takes the value 1. The Heaviside function can be used to represent an "Off-On" function.See link for more.The Heaviside function is a discontinuous step function. It is 0 for all values less than some specific value. At and after that value, it takes the value 1. The Heaviside function can be used to represent an "Off-On" function.See link for more.The Heaviside function is a discontinuous step function. It is 0 for all values less than some specific value. At and after that value, it takes the value 1. The Heaviside function can be used to represent an "Off-On" function.See link for more.
Is the relation (-1 4) (2 7) (37) a function?
Yes, there is only one y value for each x value.
What is the value of unit step function at t equals 0?
The unit step function at t=0 is defined to have a value of 1.
What is the example of the range and domain in a function?
A function is a mapping from one set to another. It may be many-to-one or one-to-one. The first of these sets is the domain and the second set is the range. Thus, for each value x in the domain, the function allocates the value f(x) which is a value in the range. For example, if the function is f(x) = x^2 and the domain is the integers in the interval [-2, 2], then the range is the set [0, 1, 4].
