Describe the behaviour of the graph of the function as x → – ∞ and as x → ∞.
Question
Describe the behaviour of the graph of the function as x → – ∞ and as x → ∞.
Solution
To answer this question, we first need to know the function. The behavior of the graph as x approaches negative infinity (-∞) or positive infinity (∞) depends on the specific function.
For example, if we have a linear function like f(x) = mx + b, as x approaches -∞, the function will go to ∞ if m is positive and will go to -∞ if m is negative. As x approaches ∞, the function will go to ∞ if m is positive and will go to -∞ if m is negative.
For a quadratic function like f(x) = ax^2 + bx + c, as x approaches -∞ or ∞, the function will go to ∞ if a is positive and will go to -∞ if a is negative.
For a rational function like f(x) = (ax + b) / (cx + d), as x approaches -∞ or ∞, the function will approach a/c.
So, to give a specific answer, we need to know the function.
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