To draw a graph of a function h(x) with two stationary points, one singular point, domain (-∞, ∞), and no relative extremum, we can follow these steps:
1. Start by understanding the meaning of stationary points and singular points:
- Stationary points are points on the graph where the slope or derivative of the function is zero.
- A singular point is a point where the function is undefined or has a vertical asymptote.
2. To create a function with two stationary points, we can use a quadratic function. For example, let's use the function h(x) = x^2 - 2x + 1. This function has two stationary points because its derivative is h'(x) = 2x - 2, which equals zero when x = 1.
3. To introduce a singular point, we can add a denominator to the function. Let's modify our function to h(x) = (x^2 - 2x + 1)/(x - 3). Now, we have a singular point at x = 3 because the denominator becomes zero at that point, resulting in an undefined value.
4. The domain of the function h(x) is (-∞, ∞) because there are no restrictions on the values of x for this function.
5. To ensure there are no relative extremum points, we can check the concavity of the function. In this case, the concavity remains constant, so there are no relative extremum points.
With these steps, we have created a function h(x) = (x^2 - 2x + 1)/(x - 3) that meets all the given criteria. Now, we can proceed to graphing the function.
Note: It's important to remember that without specific constraints or additional information, there can be multiple correct answers to this question.