Math Problem Statement

Draw four graphs (A, B, C, and D) where the functions are defined for all x-values, and Graphs A, B, and C have all the following properties in the listed below: Graph A: f(-2) = 2 lim(x -> -2) f(x) = -1 The line x = -2 is a vertical asymptote. Graph B: f(0) = 1 f is continuous at x = 0. Graph C: f(3) = 4 lim(x -> 3+) f(x) = 4 lim(x -> 3-) f(x) = 2 For Graph D, draw a graph with ALL the properties in ALL THREE columns.

Solution

I see you've uploaded a problem involving drawing graphs with specific properties. Here's a breakdown of the requirements for each graph:

  • Graph A:

    • f(2)=2f(-2) = 2
    • limx2f(x)=1\lim_{x \to -2} f(x) = -1
    • The line x=2x = -2 is a vertical asymptote.
  • Graph B:

    • f(0)=1f(0) = 1
    • The function is continuous at x=0x = 0.
  • Graph C:

    • f(3)=4f(3) = 4
    • limx3+f(x)=4\lim_{x \to 3^+} f(x) = 4
    • limx3f(x)=2\lim_{x \to 3^-} f(x) = 2
  • Graph D:

    • This graph should include all the properties from A, B, and C.

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Math Problem Analysis

Mathematical Concepts

Functions
Asymptotes
Continuity
Limits
Graphing Functions

Formulas

f(x) = 2
lim(x -> -2) f(x) = -1
f(0) = 1
f(3) = 4
lim(x -> 3+) f(x) = 4
lim(x -> 3-) f(x) = 2

Theorems

Continuity Theorem
Vertical Asymptote Behavior
Limit Theorem

Suitable Grade Level

Grades 9-11