True

Explanation:
When the gradient of a function is zero, it means that the derivative of the function with respect to the independent variable is zero at that point. In the case of a function of one variable, such as f(x), the derivative represents the rate of change of the function with respect to x.

When the derivative is zero, it means that the function is not changing at that point, and hence the graph of the function is parallel to the x-axis. This is because the slope of the tangent line to the graph at that point is zero, which means that the tangent line is horizontal and parallel to the x-axis.

To understand this concept further, let's consider an example:

Let's say we have a function f(x) = x^2. The derivative of this function with respect to x is f'(x) = 2x.

To find the points where the gradient is zero, we set the derivative equal to zero and solve for x:

2x = 0
x = 0

So, at x = 0, the gradient of the function is zero. This means that the function f(x) = x^2 is parallel to the x-axis at x = 0.

In general, when the gradient of a function is zero, it means that the function is not changing at that point and is parallel to the x-axis. Therefore, the statement "When the gradient of a function is zero, the function lies parallel to the x-axis" is true.