Consider the relation given by the equation y = 2x - 3. The relation of a function with a domain and codomain is specified as follows:Domain: {0, 1, 2, 3, 4, 5}Codomain: {-5, -3, -1, 1, 3, 5}Which of the following statement is correct?
Question
Consider the relation given by the equation y = 2x - 3. The relation of a function with a domain and codomain is specified as follows:Domain: {0, 1, 2, 3, 4, 5}Codomain: {-5, -3, -1, 1, 3, 5}Which of the following statement is correct?
Solution
The statement that would be correct is: "The given function y = 2x - 3 is a valid function for the specified domain and codomain."
Here's the step-by-step explanation:
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The domain of a function is the set of all possible input values (x-values), while the codomain is the set of all possible output values (y-values).
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In this case, the domain is {0, 1, 2, 3, 4, 5} and the codomain is {-5, -3, -1, 1, 3, 5}.
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If we substitute each value from the domain into the equation y = 2x - 3, we get the following results:
- For x = 0, y = 2*0 - 3 = -3
- For x = 1, y = 2*1 - 3 = -1
- For x = 2, y = 2*2 - 3 = 1
- For x = 3, y = 2*3 - 3 = 3
- For x = 4, y = 2*4 - 3 = 5
- For x = 5, y = 2*5 - 3 = 7
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As you can see, all the y-values obtained are in the codomain except for the last one (7). Therefore, the function y = 2x - 3 is not a valid function for the specified domain and codomain.
So, the correct statement is: "The given function y = 2x - 3 is not a valid function for the specified domain and codomain."
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