To find the horizontal asymptote of this function, we need to look at the highest degree terms in the numerator and denominator. Both the numerator and denominator have terms with degree 6, so we divide the coefficient of the highest degree term in the numerator (-2) by the coefficient of the highest degree term in the denominator (8). This gives us:
y = (-2/8) x^6 + 5x + 8/(8x^6 + 6x + 5)
Simplifying this, we get:
y = (-1/4) x^6 + 5x + (8/(8x^6 + 6x + 5))
As x gets very large (either positively or negatively), the x^6 term in the denominator will dominate the other terms, since its exponent is so much larger than the exponents on the other terms. This means that the denominator will grow much faster than the numerator, and the fraction as a whole will approach 0. Therefore, the horizontal asymptote of the function is y = 0.
Find the horizontal asymptote of the graph of y = Start Fraction negative 2 x superscript 6 baseline plus 5 x plus 8 over 8 x superscript 6 baseline plus 6 x plus 5 End Fraction
3 answers
it would help if you just learned how to type math!
y = (-2x^6 + 5x + 8)/(8x^6 + 6x + 5)
since the numerator and denominator are the same degree, the horizontal asymptote is the line y = -2/8
y = (-2x^6 + 5x + 8)/(8x^6 + 6x + 5)
since the numerator and denominator are the same degree, the horizontal asymptote is the line y = -2/8
are you sure