Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter8: Introduction To Functions
Section8.8: Linear And Quadratic Functions
Problem 2WE
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![**Piecewise Function Graphing Tutorial**
### Objective:
Graph the piecewise function:
\[ f(x) = \begin{cases}
2x - 1 & \text{if } x < 2 \\
x - 2 & \text{if } x \geq 2
\end{cases} \]
### Instructions:
1. **Identify the Different Functions**:
- For \( x < 2 \), the function is \( f(x) = 2x - 1 \).
- For \( x \geq 2 \), the function is \( f(x) = x - 2 \).
2. **Graph for \( x < 2 \):**
- This is a linear equation in the form \( y = mx + b \), where \( m = 2 \) and \( b = -1 \).
- Plot the line segment for \( f(x) = 2x - 1 \) only for values of \( x \) that are less than 2.
- Choose key points to plot. For example:
- When \( x = 0 \), \( y = 2(0) - 1 = -1 \).
- When \( x = 1 \), \( y = 2(1) - 1 = 1 \).
3. **Graph for \( x \geq 2 \):**
- This is a linear equation in the form \( y = mx + b \), where \( m = 1 \) and \( b = -2 \).
- Plot the line segment for \( f(x) = x - 2 \) only for values of \( x \) that are equal to or greater than 2.
- Choose key points to plot. For example:
- When \( x = 2 \), \( y = 2 - 2 = 0 \).
- When \( x = 3 \), \( y = 3 - 2 = 1 \).
4. **Combine the Graphs**:
- Use an open circle to indicate that the endpoint at \( x = 2 \) for \( f(x) = 2x - 1 \) is not included.
- Use a closed circle to indicate that the endpoint at \( x = 2 \) for \( f(x) = x - 2 \) is included.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fec5383c7-ce71-4639-9c19-f5515f12eee5%2F9712a2c4-848b-43b7-87f7-8915a4b88ff6%2Fiiq744v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Piecewise Function Graphing Tutorial**
### Objective:
Graph the piecewise function:
\[ f(x) = \begin{cases}
2x - 1 & \text{if } x < 2 \\
x - 2 & \text{if } x \geq 2
\end{cases} \]
### Instructions:
1. **Identify the Different Functions**:
- For \( x < 2 \), the function is \( f(x) = 2x - 1 \).
- For \( x \geq 2 \), the function is \( f(x) = x - 2 \).
2. **Graph for \( x < 2 \):**
- This is a linear equation in the form \( y = mx + b \), where \( m = 2 \) and \( b = -1 \).
- Plot the line segment for \( f(x) = 2x - 1 \) only for values of \( x \) that are less than 2.
- Choose key points to plot. For example:
- When \( x = 0 \), \( y = 2(0) - 1 = -1 \).
- When \( x = 1 \), \( y = 2(1) - 1 = 1 \).
3. **Graph for \( x \geq 2 \):**
- This is a linear equation in the form \( y = mx + b \), where \( m = 1 \) and \( b = -2 \).
- Plot the line segment for \( f(x) = x - 2 \) only for values of \( x \) that are equal to or greater than 2.
- Choose key points to plot. For example:
- When \( x = 2 \), \( y = 2 - 2 = 0 \).
- When \( x = 3 \), \( y = 3 - 2 = 1 \).
4. **Combine the Graphs**:
- Use an open circle to indicate that the endpoint at \( x = 2 \) for \( f(x) = 2x - 1 \) is not included.
- Use a closed circle to indicate that the endpoint at \( x = 2 \) for \( f(x) = x - 2 \) is included.
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