graph piecewise function (formatting was weird first time sorry)
5+(1/(x-1) ) if x<1
2x-4 if 1 ≤ x< 5
-1-x^2 if x ≥ 5
To graph a piecewise function, you need to split the graph into different sections based on the given conditions. In this case, we have three conditions based on the values of x:
1) When x < 1: The function is 5 + (1/(x-1)).
2) When 1 ≤ x < 5: The function is 2x - 4.
3) When x ≥ 5: The function is -1 - x^2.
To graph each section of the piecewise function, follow these steps:
1) For the first condition (x < 1):
- Choose some x-values that are less than 1.
- Plug each chosen x-value into the expression 5 + (1/(x-1)) to find the corresponding y-values.
- Plot these points on the graph.
2) For the second condition (1 ≤ x < 5):
- Choose some x-values between 1 and 5.
- Plug each chosen x-value into the expression 2x - 4 to find the corresponding y-values.
- Plot these points on the graph.
3) For the third condition (x ≥ 5):
- Choose some x-values greater than or equal to 5.
- Plug each chosen x-value into the expression -1 - x^2 to find the corresponding y-values.
- Plot these points on the graph.
Once you have plotted all the points for each condition, connect them smoothly to create the graph of the piecewise function.
Remember to label the axes and indicate any discontinuities in the graph (if applicable).