Question

The function h is given by h(x)= 2x^3/x+3 - 4/x-1 . Which of the following statements is true? A. h is equivalent to (2x^4-2x^3-4x-12)/x^2+2x-3 and has the same end behavior as the graph of y=2x^2. B. h is equivalent to (2x^3-4)/x^2+2x-3 and has the same end behavior as the graph of y=2x. C. h is equivalent to 2x^3/x + 2x^3/3 - 4/x-1 and has the same end behavior as the graph of y=2x^2. D. h is equivalent to (2x^2-2x-12)/3x-3 and has the same end behavior as the graph of y=2x.

Answer 1

None of the given options are true for the function h(x).

Step-by-step explanation:

To determine which of the given options is true for the function h(x) = 2x^3/x+3 - 4/x-1, we need to simplify the expression and compare it with the options one by one.

Starting with option A, if we simplify h(x) to (2x^4-2x^3-4x-12)/x^2+2x-3, we can see that it is not equivalent to the original expression. Therefore, option A is not true.

Next, let's simplify option B, h(x) = (2x^3-4)/x^2+2x-3. If we compare this with the original expression, we can see that it is equivalent. However, the end behavior of the graph y=2x is different from the original function h(x) because the exponents of x are different. Therefore, option B is also not true.

By the process of elimination, we can conclude that none of the given options are true for the function h(x).