Math Problem Statement

Graph the piecewise function f(x) where f(x) = -1/3x + 3 for -6 <= x <= -3 and f(x) = 4 for -3 < x < 5.

Solution

Here's the graph of the given piecewise function f(x)f(x):

  1. The blue line represents the linear segment f(x)=13x+3f(x) = -\frac{1}{3}x + 3 for 6x3-6 \leq x \leq -3.

    • The filled blue circle at x=3x = -3 indicates the endpoint where the first piece ends.
  2. The green horizontal line represents the constant value f(x)=4f(x) = 4 for 3<x<5-3 < x < 5.

    • The open green circle at x=3x = -3 indicates a discontinuity, showing that f(x)f(x) is not defined as 4 at x=3x = -3, but immediately jumps from 3 to 4 after this point.

Would you like more details on the graph or any clarifications?

Here are some related questions for further exploration:

  1. How do you find the slope of a line from its equation?
  2. How does the graph of a constant function look like, and why?
  3. What happens when there is a discontinuity in a piecewise function?
  4. How would you graph a quadratic function as part of a piecewise function?
  5. What are the conditions for a function to be continuous at a given point?

Tip: Always look at endpoints carefully when graphing piecewise functions. Some are included (closed circle), while others are not (open circle).

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Piecewise Functions
Graphing Linear Functions
Constant Functions
Discontinuities

Formulas

f(x) = -1/3x + 3
f(x) = 4

Theorems

Graphing Piecewise Functions
Continuity and Discontinuity Theorems

Suitable Grade Level

Grades 9-12