Use a graphing utility to graph the function and visually estimate the linits
h(x)= -x^2 + 4x
To graph the function h(x) = -x^2 + 4x using a graphing utility, you can follow these steps:
1. Open a graphing utility software or use an online graphing tool.
2. Set up the coordinate plane by specifying the x- and y-axis ranges.
3. Enter the equation h(x) = -x^2 + 4x into the equation input area.
4. Press the "Graph" or "Plot" button to generate the graph.
Once the graph is generated, you can visually estimate the limits of the function.
To estimate the limits visually, observe the behavior of the function as x approaches positive and negative infinite values:
- As x approaches positive infinity (∞), the function will tend towards negative infinity because the x^2 term becomes dominant and makes the overall value negative.
- As x approaches negative infinity (-∞), the function will also tend towards negative infinity since the x^2 term becomes more significant and negative.
By visually inspecting the graph, you can look for the trend of the function as it approaches these infinite values to estimate the limits.