QQuestionMathematics
QuestionMathematics
13. Select all of the following graphs which are one-to-one functions.
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Answer
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Step 1:: Examine the first graph.
A one-to-one function is also called an injective function, which means that each element in the range corresponds to exactly one element in the domain. In this graph, we see that every x-value has only one corresponding y-value, and there are no horizontal lines that intersect the graph more than once. Therefore, this function is one-to-one.
Step 2:: Examine the second graph.
This function also has the property that each x-value corresponds to only one y-value, and there are no horizontal lines that intersect the graph more than once. Therefore, this function is also one-to-one.
Step 3:: Examine the third graph.
This function appears to be a parabola, which is not one-to-one, as there are x-values that correspond to more than one y-value. For example, the point (- 1, 1) and the point (1, 1) both correspond to the same y-value of 1, but with different x-values. Therefore, this function is not one-to-one.
Step 4:: Examine the fourth graph.
This function appears to be a circle, which is also not one-to-one, as there are x-values that correspond to more than one y-value. For example, the point (- 1, 0) and the point (1, 0) both correspond to the same y-value of 0, but with different x-values. Therefore, this function is not one-to-one.
Step 5:: Examine the fifth graph.
This function appears to be a line with a negative slope, which is one-to-one, as every x-value corresponds to only one y-value, and there are no horizontal lines that intersect the graph more than once. Therefore, this function is one-to-one.
Final Answer
The one-to-one functions are the first graph, the second graph, and the fifth graph.
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