How do I sketch the function? ### Piecewise Function and Its GraphIn this example, we are given a piecewise function \( f(x) \) defined as follows:\[f(x) =\begin{cases} -x - 6 & \text{if } x \leq -3 \\-3 & \text{if } -3 < x \leq 4 \\1.5 - 7 & \text{if } x > 4 \end{cases}\]We are required to sketch the graph of this piecewise function based on the given conditions.### Analysis of Each Piece1. **For \( x \leq -3 \):** The function is \( f(x) = -x - 6 \). - This is a linear function with a negative slope. - As \( x \) decreases, \( f(x) \) increases according to the equation. 2. **For \( -3 < x \leq 4 \):** The function is \( f(x) = -3 \). - This is a constant function, meaning for all \( x \) in this interval, \( f(x) \) is always -3. 3. **For \( x > 4 \):** The function is \( f(x) = 1.5 - 7 \). - This simplifies to \( f(x) = -5.5 \), indicating another constant function where \( f(x) \) is always -5.5 for \( x \) greater than 4.### Graph ExplanationThe provided graph paper has both horizontal and vertical axes marked with grid lines. Here's how to sketch the graph based on the piecewise function:1. **For the interval \( x \leq -3 \):** - Plot the line \( f(x) = -x - 6 \). - For example, when \( x = -3 \), \( f(x) = -(-3) - 6 = 3 - 6 = -3 \). - Extend the line with that slope to the left of \( x = -3 \).2. **For the interval \( -3 < x \leq 4 \):** - Draw a horizontal line at \( f(x) = -3 \) - This extends from just greater than \( x = -3 \) to \( x = 4 \

Name: How do I sketch the function? ### Piecewise Function and Its GraphIn t
Uploaded: 2024-03-20T06:47:22.000Z
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Description: How do I sketch the function? ### Piecewise Function and Its GraphIn this example, we are given a piecewise function \( f(x) \) defined as follows:\[f(x) =\begin{cases} -x - 6 & \text{if } x \leq -3 \\-3 & \text{if } -3 < x \leq 4 \\1.5 - 7 & \text{i