for piecewise functions do I connect all the functions?
Ex:
f(x): 2+x
x less than or equal to -3
f(x): x^2
-3 less than x less than 1
f(x): 6
1 less than or equal to x
I graphed this but I don't know where to connect the lines between f(x):2+x and f(x): x^2 because at (-1,1) f(x):2+x goes through the graph of f(x):x^2. But, shouldn't I connect the point at (-3,9)(this is the start of f(x):x^2 or at (-1,1)
For piecewise functions, you do not typically connect the different segments of the line, unless there is a specific condition mentioned in the problem. In your case, each segment of the piecewise function has a specific domain range in which it is valid.
Looking at the given function:
f(x) = 2 + x, for x ≤ -3
f(x) = x^2, for -3 < x < 1
f(x) = 6, for x ≥ 1
When graphing a piecewise function, you need to plot the points for each segment and indicate the appropriate domain range.
Start by drawing a point at (-3, -1) for the first segment f(x) = 2 + x and indicate that this segment is only valid for x ≤ -3.
Next, draw a point at (1, 1) for the second segment f(x) = x^2 and indicate that this segment is valid for -3 < x < 1.
Finally, draw a horizontal line at y = 6 for the third segment f(x) = 6, indicating that this segment is only valid for x ≥ 1.
Remember that these segments are separate and do not connect unless there is a specified condition. In your case, there is no specific condition mentioned that would require connecting the lines. So, you would not connect the points at (-3, 9) or (-1, 1) to any other part of the graph.