Math Problem Statement
Given the following piecewise function,
f(−7)= Blank 1 Question 22
f(−1)= Blank 2 Question 22
f(0)= Blank 3 Question 22
Solution
The piecewise function is defined as follows:
3x - 1, & \text{if } x \geq -1 \\ -5, & \text{if } x < -1 \end{cases}$$ Let's evaluate the function for the given values of $$x$$: 1. **$$f(-7)$$:** Since $$-7 < -1$$, we use the second piece of the function: $$f(-7) = -5$$ 2. **$$f(-1)$$:** Since $$-1 \geq -1$$, we use the first piece of the function: $$f(-1) = 3(-1) - 1 = -3 - 1 = -4$$ 3. **$$f(0)$$:** Since $$0 \geq -1$$, we use the first piece of the function: $$f(0) = 3(0) - 1 = 0 - 1 = -1$$ So, the values are: $$\begin{align*} f(-7) &= -5 \\ f(-1) &= -4 \\ f(0) &= -1 \end{align*}$$ Would you like further details or have any questions? Here are 5 questions related to this topic: 1. How do you determine which part of a piecewise function to use? 2. What is the significance of the inequality in a piecewise function? 3. How would the function change if the condition was $$x > -1$$ instead of $$x \geq -1$$? 4. What are the key differences between continuous and discontinuous piecewise functions? 5. How would you graph this piecewise function? **Tip:** Always pay close attention to the inequality signs in piecewise functions to correctly determine which expression to use for evaluation.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise functions
Formulas
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Theorems
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Suitable Grade Level
Grades 9-12