\( f(x)=\frac{2 x^{4}}{x^{2}+8} \) Part 1 of 3 Equation(s) of the vertical asymptote(s): None Equation(s) of the horizontal asymptote(s): None Equation(s) of the slant asymptote(s): None \( 1 / 3 \) Part 2 of 3 \( x \)-intercept(s): \( \square \) (Write your answer as an ordered pair.) (Write your answer as an ordered pair.)

To find the \( x \)-intercept(s) of the function \( f(x)=\frac{2 x^{4}}{x^{2}+8} \), we need to set \( f(x) = 0 \). This occurs when the numerator is 0. Therefore, we solve \( 2x^4 = 0 \), which gives us \( x = 0 \). The corresponding \( y \)-coordinate is \( f(0) = 0 \). So, the ordered pair for the \( x \)-intercept is \( (0, 0) \). Now, for a bit of fun, did you know that the concept of intercepts dates back to ancient civilizations? The Babylonians and Greeks were already dabbling in geometric representations of numbers, much like we do with intercepts on a graph! Additionally, having a strong grasp of intercepts and asymptotic behavior in functions can be crucial for real-world applications. Whether you're designing a roller coaster or analyzing population growth, understanding how functions behave at certain points can help you make informed decisions!