Final answer:
The domain of the function F(x)=2x²-5/x² is all real numbers except zero. The range is all real numbers, as indicated by the behavior of the graph. The graph should be labeled and scaled appropriately to show the function's behavior across the domain.
Step-by-step explanation:
To find the domain and range of the function F(x) = 2x² - 5/x², we first need to graph the function. This function is not defined when x = 0 because the denominator of the fraction becomes zero, which is not allowed in mathematics. Therefore, the domain of F(x) is all real numbers except zero, often written as x ∈ ℝ, x ≠ 0. To determine the range, we look at the graph of the function. Because the numerator of the function increases without bound as x gets very large or very small (neglecting zero), the function approaches infinity and negative infinity. Therefore, the function doesn't have a maximum or minimum, and the range is all real numbers. We label the graph with f(x) along the y-axis and x along the x-axis, using an appropriate scale that excludes zero from the domain. For example, we could show values of x from -20 to 20 (excluding 0) and choose a similar scale for f(x) to reflect the behavior of the function.