Math Problem Statement

For the function f whose graph is given, state the value of each quantity, if it exists. If it does not exist, explain why.

Solution

The image contains a calculus problem asking for the limits and values of a function f(x)f(x) based on its graph. The specific questions are:

  1. For the function ff whose graph is given, state the value of each quantity, if it exists. If it does not exist, explain why:
  • (a) limx1f(x)\lim\limits_{x \to 1} f(x)
  • (b) limx3f(x)\lim\limits_{x \to 3^-} f(x)
  • (c) limx3+f(x)\lim\limits_{x \to 3^+} f(x)
  • (d) limx3f(x)\lim\limits_{x \to 3} f(x)
  • (e) f(3)f(3)

There's also a graph shown in the lower part of the image, which represents the function f(x)f(x), but the details of the graph are slightly unclear. Could you confirm the graph's characteristics around x=1x = 1 and x=3x = 3 (like any discontinuities, jumps, or if the graph approaches any specific values at those points)? This will help in interpreting the limits and the value of f(3)f(3).

Let me know if you want me to try interpreting the graph more closely or if you have clearer information!

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Math Problem Analysis

Mathematical Concepts

Limits
Piecewise Functions
Continuity

Formulas

Limit Definition: lim(x → c) f(x)
One-sided Limits

Theorems

Limit Theorems
Continuity and Discontinuity Theorems

Suitable Grade Level

Grades 11-12 (Pre-Calculus or Calculus I)