QQuestionMathematics
QuestionMathematics
Which of the following functions has a horizontal asymptote at y = 2?
| 10 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 2 |
| 1 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
| - 10 | - 9 | - 8 | - 7 | - 6 | - 5 | - 4 | - 3 | - 2 | - 1 | 1 |
| - 2 | - 2 | - 3 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| - 3 | - 4 | - 5 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| - 4 | - 5 | - 6 | - 7 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| - 5 | - 7 | - 8 | - 9 | - 10 | 1 | 2 | 3 | 4 | 5 | 6 |
| - 6 | - 9 | - 10 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| 10 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 2 |
| 1 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
| - 10 | - 9 | - 8 | - 7 | - 6 | - 5 | - 4 | - 3 | - 2 | - 1 | 1 |
| - 2 | - 2 | - 3 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| - 3 | - 4 | - 5 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| - 4 | - 5 | - 6 | - 7 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| - 5 | - 7 | - 8 | - 9 | - 10 | 1 | 2 | 3 | 4 | 5 | 6 |
| - 6 | - 9 | - 10 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| 10 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 2 |
| 1 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
| - 10 | - 9 | - 8 | - 7 | - 6 | - 5 | - 4 | - 3 | - 2 | - 1 | 1 |
| - 2 | - 2 | - 3 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| - 3 | - 4 | - 5 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| - 4 | - 5 | - 6 | - 7 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| - 5 | - 7 | - 8 | - 9 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| - 6 | - 9 | - 10 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
12 months agoReport content
Answer
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Step 1:: Identify the function from the given table
From the table, we can see that the output values correspond to the function's values for different input values. We need to identify the pattern to find the function. It seems that the function alternates between two different linear functions, one with positive slope and one with negative slope. Let's denote the function as f(2$): For positive x values, the function is f(2$) = 10 - x. For negative x values, the function is f(2$) = x - 2.
Step 2:: Determine the horizontal asymptote
A horizontal asymptote is a y-value that the function approaches as x approaches positive or negative infinity. For rational functions, the horizontal asymptote can be determined by looking at the degrees of the numerator and denominator. However, in this case, we have a piecewise function, so we need to check the limits for x approaching positive and negative infinity separately. For large positive x values, the function approaches f(2$) = 10 - x. As x approaches positive infinity, 10 - x approaches -infinity. For large negative x values, the function approaches f(2$) = x - 2. As x approaches negative infinity, x - 2 approaches negative infinity. Since the function doesn't approach a specific y-value as x approaches positive or negative infinity, there is no horizontal asymptote. However, the question asks for the horizontal asymptote at y = 2. This means that the table provided might be truncated or modified to make it appear as if there is a horizontal asymptote at y = 2. Based on the given information, there is no justification for a horizontal asymptote at y = 2.
Final Answer
There is no horizontal asymptote at y = 2 for the given function.
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