use the leading coefficient test to determine whether y-infinity or y- -infinity as x - -infinity for the function
y=8x^9-888x^4
To use the leading coefficient test, we look at the power of x with the largest exponent, which is 9 in this case.
If the degree of the polynomial is odd (in this case, 9), then as x approaches negative infinity, y will also approach negative infinity.
Therefore, y will approach negative infinity as x approaches negative infinity for the function y = 8x^9-888x^4.
To determine whether y approaches positive infinity or negative infinity as x approaches negative infinity for the function y = 8x^9 - 888x^4, we need to consider the leading term of the function.
The leading term is the term with the highest power of x, which in this case is 8x^9. The leading coefficient is the coefficient of the leading term, which is 8.
The leading coefficient test states that if the leading coefficient is positive, then as x approaches negative infinity, y approaches positive infinity. Conversely, if the leading coefficient is negative, then as x approaches negative infinity, y approaches negative infinity.
In this case, the leading coefficient is positive (8), therefore, as x approaches negative infinity, y approaches positive infinity.
To use the leading coefficient test to determine the behavior of a function as x approaches negative infinity, we need to look at the degree and the leading coefficient of the polynomial function.
In the given function, y = 8x^9 - 888x^4, the degree of the function is 9, which is odd.
The leading coefficient is the coefficient of the term with the highest degree, in this case, 8.
For functions with odd degrees:
- If the leading coefficient is positive (+), then as x approaches negative infinity, y approaches positive infinity (y → +∞).
- If the leading coefficient is negative (-), then as x approaches negative infinity, y approaches negative infinity (y → -∞).
Since the leading coefficient in our given function is positive (+8), we can conclude that as x approaches negative infinity, y approaches positive infinity (y → +∞).
Therefore, as x approaches negative infinity, y goes to positive infinity.