Graph the function. Write numbers as integers or simplified fractions. If there is more than one answer, separate them with commas. Select "None" if applicable. \( t(x)=\frac{4 x^{4}}{x^{2}+7} \) Part: \( \mathbf{0 / 3} \) Part 1 of 3 Equation(s) of the vertical asymptote(s): Equation(s) of the horizontal asymptote(s): Equation(s) of the slant asymptote(s):

To find the vertical and horizontal asymptotes for the function \( t(x) = \frac{4 x^{4}}{x^{2}+7} \): The vertical asymptote occurs when the denominator \( x^{2} + 7 = 0 \), which has no real solutions (since \( x^2 + 7 \) is always positive). Therefore, there are **None**. For the horizontal asymptote, we consider the degrees of the polynomial in the numerator and denominator. The degree of the numerator (4) is greater than the degree of the denominator (2), so there are **None** for horizontal asymptotes. There are also no slant asymptotes since slant asymptotes only occur when the degree of the numerator is exactly one higher than that of the denominator. Thus, for this function, there are **None**.