Answer:
Explanation:
The statement that describes the function f(x) = 4x^3 + 8 is:
A. The function does not have an inverse function because f(x) fails the vertical line test.
To see why this is the correct answer, let's first define what the vertical line test and the horizontal line test are.
Vertical line test: A function passes the vertical line test if any vertical line intersects the graph of the function at most once. This means that no two points on the graph have the same x-coordinate.
Horizontal line test: A function passes the horizontal line test if any horizontal line intersects the graph of the function at most once. This means that no two points on the graph have the same y-coordinate.
Now, let's look at the function f(x) = 4x^3 + 8. We can graph this function by plotting points or by using a graphing calculator. The graph of the function looks like a curve that goes up and to the right.
If we draw a vertical line anywhere on the graph, we can see that it intersects the graph at most once, which means that f(x) passes the vertical line test. However, if we draw a horizontal line on the graph, we can see that it intersects the graph at more than one point. This means that f(x) fails the horizontal line test.
The fact that f(x) fails the horizontal line test tells us that there are some values of y that correspond to more than one value of x. This means that f(x) is not a one-to-one function, and therefore it does not have an inverse function.
Therefore, the correct statement that describes the function f(x) is:
A. The function does not have an inverse function because f(x) fails the vertical line test.