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How do you know that the value of each angle put into a trigonometric function results in exactly one output value?
The value of each angle put into a trigonometric function results in exactly one output value, because that angle represents a single set of x and y coordinates on the ray at the end of the unit circle. Since the trigonometric functions are all defined as the ratio of x and/or y and/or 1, there can only be one output value for each angle.
However, the reverse is not true. As an example, tangent is defined as sine over cosine, or y over x. This means that an angle of theta plus 180 degrees generates the same value, because y over x is the same as -y over -x.
What else can I help you with?
In the inverse variation function what happens to the output when the function's input is halved?
The output is doubled.
In the inverse variation function, what happens to the output when the function's input value is divided by 5?
The output is multiplied by 5.
What is the set of all possible output values of a function or relation?
The Range is the set of all possible output values of a function or relation.
In the inverse variation function what happens to the output when the functions input value is multiplied by 4?
the output is divided by 4
What term is used to describe when two functions are linked together by using output of the first function as input of second function?
function composition
If you double the input of a function and it results in half the output and if you triple the input and it results in a third of the output what can be guessed about the function?
~the function is most likely inversely proportional. ~more input results in less output.
If you double the input of a function and it results in four times the output and if you triple the input and it results in six times the output what can be guessed about the function?
more input results in more output the function is most likely directly proportional
What is an input-output relationship that has exactly one output for each input?
function
What gives exactly one output for every input?
a function
A relation with exactly one output for each input?
It's a type of function
What term means for each input their is exactly one output?
function
If you quadruple the input of a function and the resulting output is one-fourth the original output what may be true of the function?
More input results in less output. The function is inversely proportional.
What is the value that results from the substitution of a given imput into an expression or function?
An output
What is a mathematical relationship in which each input corresponds to exactly one output?
A Function
The value that results from the substitution of a given input into an expression or function?
The value that results from the substitution of a given input into an expression or function is the output. The value substituted into an expression or function is an input.
What is the function rules of input and output?
The rule is what actions (operations) the function performs. The only requirement is that for each imput there is an output and that the same input always results in the same output. (Different inputs can have the same output).
What is a rule that assigns exactly one output value to each input value?
A function is a rule which assigns exactly one output f(x) to every input x.
