Final answer:
The function y = x⁸ is best described as similar to y = x², as both are even functions with graphs that are symmetric about the y-axis and have positive values for all x, excluding x = 0.
Step-by-step explanation:
The graph of the function y = x⁸ (x to the power of eight) is best described as similar to y = x² (x squared). This is because both are even functions, meaning that their graphs are symmetric about the y-axis. For y = x⁸, when x is positive, the y value becomes very large as the power is positive and even, and when x is negative, the y value still becomes very large since a negative number raised to an even power results in a positive.
This is similar to the behavior of a quadratic function y = x², which also has a graph that opens upwards and is symmetric about the y-axis, though the steepness of the curve differs.
The graph of the function y = x⁸ is most similar to the graph of y = x². Both functions have an even exponent, which means that the graph will be symmetric about the y-axis. Additionally, both functions have positive leading coefficients, which means that the graph will open upward.
For example, when we substitute specific values of x into the function y = x⁸, we get corresponding values of y:
x = -2: y = (-2)⁸ = 256
x = -1: y = (-1)⁸ = 1
x = 1: y = (1)⁸ = 1
x = 2: y = (2)⁸ = 256
The resulting points create a U-shaped curve that resembles the graph of y = x².