f(x) = -3/-x+21-4 if x <3 √x+4 +3 if x 3 • to graph fix) = -31-x+2) -4: take the graph of which looks like this. Shift it shift it flip it down? make it units units yes/no? wider/naslower? yes/no? acrossy? units. units_ up/down? right/Kft? • to graph f/x) = √ √x+4+3 2 take the graph of: which looks like this: shift it shift it flip it down? make it y-int: wider/narrower? yes/no? up / down? acrossy ? right/left? yes/no?
f(x) = -3/-x+21-4 if x <3 √x+4 +3 if x 3 • to graph fix) = -31-x+2) -4: take the graph of which looks like this. Shift it shift it flip it down? make it units units yes/no? wider/naslower? yes/no? acrossy? units. units_ up/down? right/Kft? • to graph f/x) = √ √x+4+3 2 take the graph of: which looks like this: shift it shift it flip it down? make it y-int: wider/narrower? yes/no? up / down? acrossy ? right/left? yes/no?
f(x) = -3/-x+21-4 if x <3 √x+4 +3 if x 3 • to graph fix) = -31-x+2) -4: take the graph of which looks like this. Shift it shift it flip it down? make it units units yes/no? wider/naslower? yes/no? acrossy? units. units_ up/down? right/Kft? • to graph f/x) = √ √x+4+3 2 take the graph of: which looks like this: shift it shift it flip it down? make it y-int: wider/narrower? yes/no? up / down? acrossy ? right/left? yes/no?
Sketch the graph of each piece-wise defined function; show all work.
Transcribed Image Text:### Transcription of Mathematical Function Analysis
This document outlines how to graph piecewise functions with specified transformations. Let's examine the components:
#### Function Definition:
The function \( f(x) \) is defined as two separate expressions, depending on the value of \( x \):
- \( f(x) = -3| -x + 2 | - 4 \) for \( x < 3 \)
- \( f(x) = \frac{1}{2} \sqrt{x + 4} + 3 \) for \( x > 3 \)
#### Graphing Instructions:
For each piece of the function, follow these steps to graph:
1. **Piece 1: \( f(x) = -3| -x + 2 | - 4 \)**
- **Base Graph:** Identify the base graph of \(| -x + 2 |\).
- **Transformations:**
- **Shift vertically:** Determine the number of units and direction (up/down).
- **Shift horizontally:** Identify the number of units and direction (right/left).
- **Flip vertically:** Determine if it flips over the x-axis (yes/no).
- **Flip horizontally:** Determine if it flips over the y-axis (yes/no).
- **Stretch/Compress:** Indicate if it becomes wider or narrower.
- **Y-intercept:** Calculate the y-intercept.
2. **Piece 2: \( f(x) = \frac{1}{2} \sqrt{x + 4} + 3 \)**
- **Base Graph:** Identify the base graph of \(\sqrt{x}\).
- **Transformations:**
- **Shift vertically:** Determine the number of units and direction (up/down).
- **Shift horizontally:** Identify the number of units and direction (right/left).
- **Flip vertically:** Determine if it flips over the x-axis (yes/no).
- **Flip horizontally:** Determine if it flips over the y-axis (yes/no).
- **Stretch/Compress:** Indicate if it becomes wider or narrower.
- **Y-intercept:** Calculate the y-intercept.
These guidelines help you correctly apply transformations to graph each piece of the function based on their respective conditions.
Definition Definition Group of one or more functions defined at different and non-overlapping domains. The rule of a piecewise function is different for different pieces or portions of the domain.
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