Draw a graph for the function f(x)=2*⌈x⌉
With the domain -2<x<=1
To draw a graph for the function f(x) = 2*⌈x⌉ with the given domain, follow these steps:
1. Determine the range of x values that fall within the specified domain -2 < x ≤ 1.
In this case, the values of x that satisfy the domain restriction are -2 < x ≤ 1.
2. Choose a set of values within the specified x range (-2 < x ≤ 1) to plot on the graph.
For simplicity, we can select a few representative values, such as -1.5, -1, -0.5, 0, and 0.5.
3. Calculate the corresponding values of f(x) for each selected value of x using the given function f(x) = 2*⌈x⌉.
We apply the ceiling function ⌈x⌉ to each x-value and then multiply by 2:
- f(-1.5) = 2*⌈-1.5⌉ = 2*(-1) = -2
- f(-1) = 2*⌈-1⌉ = 2*(-1) = -2
- f(-0.5) = 2*⌈-0.5⌉ = 2*(0) = 0
- f(0) = 2*⌈0⌉ = 2*(0) = 0
- f(0.5) = 2*⌈0.5⌉ = 2*(1) = 2
4. Plot the calculated points on the graph.
The x-values will be along the x-axis, and the corresponding f(x) values will be on the y-axis.
- Plot (-1.5, -2)
- Plot (-1, -2)
- Plot (-0.5, 0)
- Plot (0, 0)
- Plot (0.5, 2)
5. Connect the plotted points with a smooth curve.
Since the function f(x) = 2*⌈x⌉ is not continuous due to the ceiling function, the graph will consist of individual points instead of a continuous curve. Therefore, do not connect the points with a curve.
6. Label the x and y axes accordingly.
The resulting graph will show a series of points at (-1.5, -2), (-1, -2), (-0.5, 0), (0, 0), and (0.5, 2), representing the function f(x)=2*⌈x⌉ for the given domain -2 < x ≤ 1.