f(x)=[2x-1] graph the function state the range and domain.
To graph the function f(x) = 2x - 1, we can start by plotting a few points and connecting them to create a line.
Let's choose some values for x and find their corresponding y-values:
When x = -2, f(-2) = 2(-2) - 1 = -4 - 1 = -5.
So, we have the point (-2, -5).
When x = 0, f(0) = 2(0) - 1 = 0 - 1 = -1.
So, we have the point (0, -1).
When x = 2, f(2) = 2(2) - 1 = 4 - 1 = 3.
So, we have the point (2, 3).
Now, plot these points on a graph and connect them with a straight line:
|
|
|
| *
| *
| *
---------------
-2 0 2
By extending the line in both directions, we can see that it continues indefinitely.
The domain of this function, in this case, is all real numbers because we can substitute any real number for x, and the function will provide an output.
The range of this function is also all real numbers because the line extends infinitely in both directions on the y-axis, covering all possible values of f(x).
So, to summarize:
Domain: All real numbers (or (-∞, ∞))
Range: All real numbers (or (-∞, ∞))