What is the Range of this Function?
Definition of Range
The range of a function is the set of all possible output values (y-values) that the function can produce. In other words, it is the set of all values that the function can “reach” or “hit” when you plug in different input values (x-values).
Example
Let’s say we have the function f(x) = x^2. If we plug in different values of x, we get different values of y:
- f(0) = 0^2 = 0
- f(1) = 1^2 = 1
- f(2) = 2^2 = 4
- f(3) = 3^2 = 9
- …
So the range of this function is the set of all possible y-values, which is {0, 1, 4, 9, …}.
Finding the Range
There are different methods for finding the range of a function, depending on the type of function and the information given. Here are some general steps:
- Find the domain of the function, which is the set of all possible input values (x-values).
- Use algebraic or graphical methods to determine the output values (y-values) that correspond to the domain.
- Write the range as a set of numbers or a description of the pattern.
For example, if we have the function g(x) = 2x – 1, we can:
- The domain is all real numbers, since we can plug in any value of x.
- We can use a table or a graph to see that the output values range from negative infinity to positive infinity, since the slope is positive and the y-intercept is negative.
- So the range is (-∞, ∞), which means all real numbers.
Conclusion
The range of a function is an important concept in mathematics, as it helps us understand the behavior and limitations of functions. By knowing the range, we can determine whether a function is one-to-one, onto, or neither, and we can use it to solve problems in various fields, such as physics, engineering, and economics. So next time you encounter a function, don’t forget to ask yourself: what is the range of this function?
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2.What is the range of this function? – Brainly.com
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- Descriptions: We know that the range of a function is the set of all the elements of the co-domain which are associated to at least one of the elements of …
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3.What is the range of this function? – Brainly.com
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- Descriptions: Answer: The correct range is B. The range is -infinity < y < 4. Explore all similar …
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4.What is the range of the function? – Brainly.com
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- Descriptions: Answer: · The range is all real numbers greater than or equal to 2 · Step-by-step explanation: · the range of the function starts at 2 and goes on …
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5.What is the range of this function? – Brainly.com
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- Descriptions: The range of a function is the set of all output values . In the given diagram , it can be seen that all the values in domain {-1,4,8 …
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6.what is the range of this function – Brainly.com
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- Descriptions: Range is the set of y values for which the function is defined. Hence, in order to find the range we see the y values in the given table.
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- Descriptions: The range is the y-values, which is all of he numbers is the second column , {-3,0,4,6} , so the answer would be B. Explore all similar answers.
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8.what is the range of the function on the graph – Brainly.com
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- Descriptions: The range of a function refers to all the possible values y could be. When looking at the graph, we see points with y-values ranging from negative infinity …
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- Descriptions: The range of a function is the set of its possible output values. Step-by-step explanation: For example, for the function f(x)=x2 on the domain of all real …
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