Solving Piecewise Function: f(-1), f(0), and f(2)

Math Problem Statement

Given the piecewise function f(x) = {7x - 6 if x < 0, 7x - 12 if x >= 0}, calculate the values for f(-1), f(0), and f(2).

We are given a piecewise function:

\begin{cases} 7x - 6 & \text{if } x < 0 \\ 7x - 12 & \text{if } x \geq 0 \end{cases}$$ Now, let's evaluate the function for the given values: 1. **$$f(-1)$$**: Since $$-1 < 0$$, we use the first part of the function $$f(x) = 7x - 6$$. $$f(-1) = 7(-1) - 6 = -7 - 6 = -13$$ So, $$f(-1) = -13$$. 2. **$$f(0)$$**: Since $$0 \geq 0$$, we use the second part of the function $$f(x) = 7x - 12$$. $$f(0) = 7(0) - 12 = 0 - 12 = -12$$ So, $$f(0) = -12$$. 3. **$$f(2)$$**: Since $$2 \geq 0$$, we again use the second part of the function $$f(x) = 7x - 12$$. $$f(2) = 7(2) - 12 = 14 - 12 = 2$$ So, $$f(2) = 2$$. ### Final Results: - $$f(-1) = -13$$ - $$f(0) = -12$$ - $$f(2) = 2$$ Would you like any further clarifications or details? Here are 5 related questions: 1. How do we identify which piece of a piecewise function to use for a given input? 2. What happens if the function was defined differently for $$x = 0$$? 3. Can a piecewise function have more than two pieces? 4. How do we graph a piecewise function like this one? 5. What are some real-life applications of piecewise functions? **Tip:** Always check the boundary conditions in a piecewise function to ensure you use the correct piece of the function based on the input.

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Piecewise Functions
Linear Equations

f(x) = 7x - 6 if x < 0
f(x) = 7x - 12 if x >= 0

Grades 8-10

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