Math Problem Statement

CSMATH1 Practice Exercise 2 (1).pdf

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Solution

Your document contains a set of mathematical problems categorized into four sections:

  1. Graphing Functions: You need to draw graphs, identify domain, and range for given functions.
  2. Limits: Evaluate limits, including piecewise functions and rational functions.
  3. Continuity: Determine whether functions are continuous or discontinuous at given points and classify discontinuities.
  4. Finding Points of Continuity: Identify values of xx where given functions are continuous.

Would you like help solving specific problems, or would you like a step-by-step explanation of a particular section?

Here are five relevant questions that build on your document:

  1. How do you find the domain and range of a function algebraically?
  2. What are common strategies for graphing square root, absolute value, and piecewise functions?
  3. How do you determine if a limit exists for a given function?
  4. What are the different types of discontinuities in a function?
  5. How do you redefine a function to make it continuous at a given point?

Tip: When evaluating limits, always check for indeterminate forms (like 00\frac{0}{0}) and use algebraic simplifications such as factoring or L'Hôpital's rule when necessary.

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Math Problem Analysis

Mathematical Concepts

Graphing Functions
Limits
Continuity
Piecewise Functions
Rational Functions

Formulas

Limit Laws
Piecewise Function Definitions
Domain and Range Calculations

Theorems

Limit Theorem
Continuity Theorem

Suitable Grade Level

Grades 11-12