QQuestionAnatomy and Physiology
QuestionAnatomy and Physiology
# Graph each function. Identify the domain and range. (Example 1)
1. $g(x)=\left\{\begin{array}{c}- 3 \text { if } x \leq- 4 \\ x \text { if }- 4<x<2 \\ -x+ 6 \text { if } x \geq 2\end{array}\right.$
2. $f(x)=\left\{\begin{array}{c}8 \text { if } x \leq- 1 \\ 2 x \text { if }- 1<x<4 \\ - 4 -x \text { if } x \geq 4\end{array}\right.$
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Step 1I'll solve this step by step, carefully following the LaTeX formatting guidelines:
Problem 1: $$g(x)=\left\{\begin{array}{c}-3 \text{ if } x \leq-4 \ x \text{ if }-4<x<2 \ -x+6 \text{ if } x \geq 2\end{array}\right.
Step 2: Analyze the Piecewise Function
- The function $$g(x)$$ is defined in three different parts:
Final Answer
- Domain: (-\infty, \infty) - Range: [- 3, 6] Problem 2: f(x)=\left\{\begin{array}{c}8 \text{ if } x \leq- 1 \ 2x \text{ if } - 1<x<4 \ - 4 -x \text{ if } x \geq 4\end{array}\right. Step 1: Analyze the Piecewise Function - The function f(x) is defined in three different parts: 1. 8 when x \leq - 1 2. 2x when - 1 < x < 4 3. - 4 -x when x \geq 4 Step 2: Determine Domain - The domain includes all real numbers where the function is defined - Domain: (-\infty, \infty) Step 3: Determine Range - For x \leq - 1: f(x) = 8 - For - 1 < x < 4: f(x) = 2x (ranges from - 2 to 8) - For x \geq 4: f(x) = - 4 -x (ranges from - 8 to 0) - Domain: (-\infty, \infty) - Range: [- 8, 8]
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