Math Problem Statement
Graph the following piecewise function on the axes provided:
f(x) = { x + 3, for -1 < x ≤ 2
-x + 9, for 2 < x ≤ 6
Click and drag to make a line. Click the line to delete it. Click on an endpoint of a line to change it.
Solution
To graph the given piecewise function, follow these steps:
Function:
- for
- for
Steps to Graph:
1. For ():
- Start by substituting the boundary points:
- At :
- At :
- Plot the segment from (open circle) to (closed circle).
2. For ():
- Substituting the boundary points:
- At : (open circle at ).
- At : (closed circle at ).
- Plot the segment from (open circle) to (closed circle).
Graph:
- Draw the first line segment for , from to .
- Draw the second line segment for , from to .
Would you like a detailed illustration or assistance in sketching?
Here are five relevant follow-up questions:
- Would you like a table of values for each piece of the function?
- Should I provide step-by-step calculations for each segment?
- Do you need help identifying open and closed points on the graph?
- Are you familiar with how to plot piecewise functions?
- Would a digital or graphical representation of this be more helpful?
Tip: Always check the domain boundaries carefully to ensure you plot open and closed circles correctly!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Linear Functions
Domain and Range
Graphing
Formulas
f(x) = x + 3
f(x) = -x + 9
Theorems
Graphing Linear Equations
Domain and Range Representation
Suitable Grade Level
Grades 8-10