Week 3 Assignment Graphs and Functions

Week 3: Graphs and Functions Assignment

Textbook: OpenStax Intermediate Algebra
Topics: Chapter 3 (Graphing Linear Equations) & (Functions)

📚 Learning Objectives

By the end of this week, you should be able to:

• Graph linear equations using tables, intercepts, and slope-intercept form.
• Identify functions from graphs, tables, or equations.
• Evaluate functions and understand domain and range.

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🔢 Part 1: Practice Problems

Solve the following problems. Show all your work clearly.

1. Graphing Linear Equations
   a. Graph the equation: y=2x−3y = 2x – 3y=2x−3
   b. Use the intercepts to graph: 3x+2y=63x + 2y = 63x+2y=6
2. Slope and Intercepts
   a. Find the slope and y-intercept of: y=−12x+4y = -\frac{1}{2}x + 4y=−21​x+4
   b. Find the slope between the points (2, 5) and (6, -3)
3. Identifying Functions
   a. Determine if the relation is a function:
   {(2,3),(4,5),(2,6),(7,8)}\{(2,3), (4,5), (2,6), (7,8)\}{(2,3),(4,5),(2,6),(7,8)}
   b. Explain your reasoning.
4. Function Notation and Evaluation
   a. Let f(x)=3×2−2x+1f(x) = 3x^2 – 2x + 1f(x)=3×2−2x+1. Find:
   • f(0)f(0)f(0)
   • f(2)f(2)f(2)
   • f(−1)f(-1)f(−1)
     b. Identify the domain and range of the function from your results.

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💬 Part 2: Assignment

Respond to the prompt below and reply to two classmates.

Graphs help us visualize relationships between variables, while functions describe how one quantity depends on another. Think about a real-life situation (such as budgeting, speed and time, or tracking fitness goals) where graphing and functions could help you solve a problem or make a decision.

Describe your example and explain how a graph or function would be useful in that situation.

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📅 Due Dates

• Part 1 (Practice Problems): Submit by
• Part 2 (Discussion):
  • Initial post by
  • Replies to classmates by