**Title: Finding Points of Intersection of Functions** **Objective:** Find the points of intersection of the graphs of the functions \( f(x) \) and \( g(x) \). **Functions Given:** - \( f(x) = x^2 - 2x + 2 \) - \( g(x) = \frac{1}{2}x + \frac{1}{2} \) **Instructions:** Determine the intersection points by solving the equation \( f(x) = g(x) \). **Equation:** Set the equations equal to each other: \[ x^2 - 2x + 2 = \frac{1}{2}x + \frac{1}{2} \] Solve for \( x \) and use these values to find the corresponding \( y \) values for each function. Record the intersection points as coordinates \((x, y)\). **Solution Fields:** - \((x, y) = ( \text{ }, \text{ })\) (for smaller x-value) - \((x, y) = ( \text{ }, \text{ })\) (for larger x-value) **Resources:** - Read It - Watch It **Submission:** Enter your solutions in the fields provided and submit them for evaluation.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Title: Finding Points of Intersection of Functions**

**Objective:**
Find the points of intersection of the graphs of the functions \( f(x) \) and \( g(x) \).

**Functions Given:**
- \( f(x) = x^2 - 2x + 2 \)
- \( g(x) = \frac{1}{2}x + \frac{1}{2} \)

**Instructions:**
Determine the intersection points by solving the equation \( f(x) = g(x) \).

**Equation:**
Set the equations equal to each other:
\[ x^2 - 2x + 2 = \frac{1}{2}x + \frac{1}{2} \]

Solve for \( x \) and use these values to find the corresponding \( y \) values for each function. Record the intersection points as coordinates \((x, y)\).

**Solution Fields:**
- \((x, y) = ( \text{ }, \text{ })\) (for smaller x-value)
- \((x, y) = ( \text{ }, \text{ })\) (for larger x-value)

**Resources:**
- Read It
- Watch It

**Submission:**
Enter your solutions in the fields provided and submit them for evaluation.
Transcribed Image Text:**Title: Finding Points of Intersection of Functions** **Objective:** Find the points of intersection of the graphs of the functions \( f(x) \) and \( g(x) \). **Functions Given:** - \( f(x) = x^2 - 2x + 2 \) - \( g(x) = \frac{1}{2}x + \frac{1}{2} \) **Instructions:** Determine the intersection points by solving the equation \( f(x) = g(x) \). **Equation:** Set the equations equal to each other: \[ x^2 - 2x + 2 = \frac{1}{2}x + \frac{1}{2} \] Solve for \( x \) and use these values to find the corresponding \( y \) values for each function. Record the intersection points as coordinates \((x, y)\). **Solution Fields:** - \((x, y) = ( \text{ }, \text{ })\) (for smaller x-value) - \((x, y) = ( \text{ }, \text{ })\) (for larger x-value) **Resources:** - Read It - Watch It **Submission:** Enter your solutions in the fields provided and submit them for evaluation.
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