To determine the end behavior of the function j(x) = 12x^(3/5) - 27x/5, we can analyze the leading term as x approaches positive and negative infinity.
The leading term in this case is 12x^(3/5) as it has the highest power of x.
1. As x approaches positive infinity:
As x becomes larger and larger positive values, the leading term 12x^(3/5) dominates the equation. Since x^(3/5) will always be positive regardless of the value of x, the product of 12 and x^(3/5) will also be positive. Hence, as x approaches positive infinity, j(x) will tend towards positive infinity.
2. As x approaches negative infinity:
As x becomes more and more negative, the leading term 12x^(3/5) will also become negative, as raising a negative number to an odd fractional power results in a negative value. Furthermore, the coefficient of the second term is negative (-27/5), so the second term will also be negative. Since both terms contribute to the negative values, as x approaches negative infinity, j(x) will tend towards negative infinity.
In conclusion, as x approaches positive infinity, j(x) will tend towards positive infinity, and as x approaches negative infinity, j(x) will tend towards negative infinity.
Consider, j(x) = 12x^3/5 - 27x/5. Describe and provide an explanation for the end behavior of j(x).
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