There are a few things to consider when trying to determine whether something represents a function or not. In mathematical terms, a function is a set of ordered pairs (x, y) where each x corresponds to a unique y. This means that a function must have a defined input and output, and the output must be unique for each input. With that in mind, let's take a look at the four options given and see if any of them fail to meet the criteria for a function.
The first option is y = 5x + 3. This is a linear equation, which means that it represents a function. The input (x) can be any real number, and the output (y) will be a corresponding real number that is five times the input plus three. So, this option does represent a function.
The second option is y = |x|. This is also a function, because the absolute value of a number will always be a non-negative real number. So, no matter what the input (x) is, the output (y) will always be a non-negative real number.
The third option is y = x^2. This is also a function, because any real number squared will always be a non-negative real number. So, no matter what the input (x) is, the output (y) will always be a non-negative real number.
The fourth option is y = sin(x). This is also a function, because the sine of any angle will always be a real number between -1 and 1. So, no matter what the input (x) is, the output (y) will always be a real number between -1 and 1.
So, all four of the options given do represent functions.
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What is the inverse of the following function?
inverse = 1/f(x)
What is the domain and range of the composition of the following function?
The domain of the composition of the function f(x)=3x+1 is all real numbers. The range is all real numbers greater than or equal to 4.
What is the domain and range of the inverse of the inverse of the following function?
The domain and range of the inverse of the inverse of the following function is the set of all real numbers.
Frequently Asked Questions
Which two lines do not represent function?
Option A,C and D
Which graph does not represent a function?
Option C does not represent function.
How do you know if something is a function or not?
The vertical line test is used to determine if something is a function. If an x-value has more than one y-value then it is not a function. It is a relation.
When is a function a function?
Only one y-element is associated with each x-element in each set of relations. Set A strictly follows the rule for being a function. Set B does not strictly follow the rule for being a function.
Why is X and Y Not a function?
X and Y are not a function because for each value of x there are more than one values of y.
Sources
- https://www.embibe.com/exams/domain-and-range-of-functions/
- https://www.coursehero.com/study-guides/ivytech-collegealgebra/determine-the-domain-and-range-of-an-inverse-function/
- https://www.math.net/inverse-function
- https://www.quora.com/Which-of-the-following-represents-a-relation-that-is-not-a-function
- https://n4vu.com/faq/what-is-the-domain-of-the-composition-function/
- https://www.onlinemathlearning.com/inverse-function-domain-range.html
- https://www.dummies.com/article/academics-the-arts/math/trigonometry/identify-the-domains-and-ranges-of-inverse-trigonometry-functions-186917/
- https://brainly.com/question/18679773
- https://brainly.com/question/8104311
- https://brainly.ph/question/613980
- https://www.symbolab.com/solver/pre-calculus-function-inverse-calculator
- https://socratic.org/questions/which-equation-does-not-represent-a-function-a-y-x-5-b-y-x-2-3-c-y-2-x-4
- https://quizlet.com/23882721/chemistry-test-8-flash-cards/
- https://math.libretexts.org/Bookshelves/Calculus/Map%3A_Calculus__Early_Transcendentals_(Stewart)/01%3A_Functions_and_Models/1.01%3A_Four_Ways_to_Represent_a_Function
- https://www.onlinemath4all.com/domain-and-range-of-inverse-trigonometric-functions.html
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